Common Hope is an educational charity supporting and empowering children and their families in Guatemala. commonhope.org In exchange for a minimum donation of $10 to the charity, I will create and name a symmetrical object for you. Donations can be made at my fund-raising site firstgiving.com. A clue to why this is my charity of choice can be found in Chapter 12: July of Finding Moonshine.

If you would like to give the group of symmetries as a birthday present or to celebrate an anniversary then leave the significant date in the comments column and I will weave the date into the construction of the symmetry group. Please email me to alert me to the fact that you have left a donation. dusautoy@maths.ox.ac.uk

Here is a list of the groups created so far that have helped change the lives of children in Guatemala.

The Anna Ruth Group Set [C[1], C[2], C[3], C[4]]=[2,0,6,1976] Corresponds to an elliptic curve of conductor 124558021948. A birthday present from her mother who sparked off the whole idea of symmetry for charity when she approached me at the Hay Literary Festival looking for an intriguing birthday present.

The Poppygon Set [C[1], C[2], C[3], C[4]]=[20,0,4,2001] Corresponds to an elliptic curve of conductor 122350161344. From Jasper James to his daughter, Poppy.

The Hollygon Set [C[1], C[2], C[3], C[4]]=[4,0,5,2003] Corresponds to an elliptic curve of conductor 520997230219. From Jasper James to his daughter, Holly.

The Vanilla Beer Group Set [C[1], C[2], C[3], C[4]]=[0,4, 0, 7] Corresponds to an elliptic curve of conductor 672. A birthday present for the 4th of July from Tony Mann.

The Josef Williamson Group Set [C[1], C[2], C[3], C[4]]=[29,0,9,1992] Corresponds to an elliptic curve of conductor 854967496638. A present from his father, a maths teacher who appreciates the beauty of such objects of the mind.

The Robert Williamson Group Set [C[1], C[2], C[3], C[4]]=[25,0,3,1994] Corresponds to an elliptic curve of conductor 34683474002. A present from his father.

The Laurie Ingram Group Set [C[1], C[2], C[3], C[4]]=[41,0,43,47] Corresponds to an elliptic curve of conductor 120505925398. A present from Peter O'Sullivan.

The Campbell Peter Group Set [C[1], C[2], C[3], C[4]]=[53,0,59,61] Corresponds to an elliptic curve of conductor 1545669582458. A present from Peter O'Sullivan.

The Sophie Group Set [C[1], C[2], C[3], C[4]]=[67,0,71,73] Corresponds to an elliptic curve of conductor 7160027904610. A present from Peter O'Sullivan.

The Roger Highfield Group Set [C[1], C[2], C[3], C[4]]=[11,0,7,1958] Corresponds to an elliptic curve of conductor 112691547970. A present from Simon Singh for Roger's 50th birthday.

The Ingrid Group Set [C[1], C[2], C[3], C[4]]=[8,0,18,2008] Corresponds to an elliptic curve of conductor 46454762148. For Ingrid: Happy 10th Anniversary from Bill Goldbloom Bloch.

The Toby William Harold Wallis Group Set [C[1], C[2], C[3], C[4]]=[6,0,1,1949] Corresponds to an elliptic curve of conductor 471074250923. A present from his son Jake.

The Roko Group Set [C[1], C[2], C[3], C[4]]=[10,0,7,1984] Corresponds to an elliptic curve of conductor 485801692003. A birthday present to Roko from Bex Walton and to celebrate completing Part III in maths at the Other Place.

The Bach Group Set [C[1], C[2], C[3], C[4]]=[0,0,0,14] Corresponds to the elliptic curve y^2=x^3+14x of conductor 12544. Betsy Devine decided there should definitely be a symmetrical shape in hyperspace named after the great J.S Bach. He already has the south polar part of Mercury poleward of latitude 65° S named after him: The Bach Qaudrant. I decided that since Bach had an obsession with the number 14 that Bach would have approved of the elliptic curve that is woven into his group. Good choice Betsy!

The David & Kevi Group Set [C[1], C[2], C[3], C[4]]=[12,0,7,2008]. Corresponds to an elliptic curve of conductor 464001236731. From David's uncle Peter.

The Leonard Wee Group Set [C[1], C[2], C[3], C[4]]=[79,0,83,89]. Corresponds to an elliptic curve of conductor 23199545316482. From Sara Hackett in Western Australia: "Just in case you don't get the drill bit named after you."

The Godfrey Allen Group Set [C[1], C[2], C[3], C[4]]=[30,0,4,1936]. Corresponds to an elliptic curve of conductor 42433127756. In memory of Stephanie Wiffen's father.

The Nuria Group Set [C[1], C[2], C[3], C[4]]=[97,0,101,103]. Corresponds to an elliptic curve of conductor 9090419634730. From David Clarke to Nuria "who has plenty of her curves of her own... ;) "

The Aisling Isla Group Set [C[1], C[2], C[3], C[4]]=[14,0,6,2007] Corresponds to an elliptic curve of conductor 21615739008. A present from Peter O'Sullivan to celebrate her first birthday.

The Debs Group Set [C[1], C[2], C[3], C[4]]=[107,0,109,113] Corresponds to an elliptic curve of conductor 175533191226758. A present from an admirer: "Can't buy me love. But, hey, what about symmetric immortality."

The Scholamancuniensis Set [C[1], C[2], C[3], C[4]]=[0,0,0,1515] Corresponds to an elliptic curve of conductor 73447200. A symmetrical shape to inspire the students at Manchester Grammar School.

The Frank Roberts Group Set [C[1], C[2], C[3], C[4]]=[10,0,11,1973] Corresponds to an elliptic curve of conductor 492267567835. For Frank Roberts, a climate physicist who finds beauty in numbers, from his wife.

The Alessandro Butteri Group Set [C[1], C[2], C[3], C[4]]=[8,0,15,1891] Corresponds to an elliptic curve of conductor 459201849243. From Alessandro Butteri's grandson.

The Olivia Andrea Group Set [C[1], C[2], C[3], C[4]]=[9,0,18,1932] Corresponds to an elliptic curve of conductor 10303285662. From Olivia Andrea's son.

The Martin Andrea Group Set [C[1], C[2], C[3], C[4]]=[7,0,13,1956] Corresponds to an elliptic curve of conductor 251620927522. A present to his mathematical brother from Alex.

The Alex Andrea Group Set [C[1], C[2], C[3], C[4]]=[5,0,22,1953] Corresponds to an elliptic curve of conductor 515219441905. For Alex Andrea, who was hoping for "an elegant picture" of the symmetrical object but will have to make do with his brother explaining the elegance of things beyond our three dimensional world.

The Åmand Group Set [C[1], C[2], C[3], C[4]]=[-1,-1,-1,5] Corresponds to an elliptic curve of conductor 10693. A present from Åmand's boyfriend Johan Falk who won the chance to name a group during my talk at ESOF 2008 in Barcelona. The coefficients mirror those in the Falk group thus providing an eternal mathematical bond between the names of Åmand and Falk.

The Laura Group Set [C[1], C[2], C[3], C[4]]=[20, 0, 11, 2004] Corresponds to an elliptic curve of conductor 110307398677. From Laura's grandmother, Brenda Maddox. An object in hyperspace to inspire Laura in her dream to become an astronaut when she grows up.

The Sinead O'Connor Group Set [C[1], C[2], C[3], C[4]]=[0, 31, 0, 7] Corresponds to an elliptic curve of conductor 104496. From Pete Wilkins to his "beautiful, mathematical wife" to celebrate their anniversary.

The Rowan Robertson Group Set [C[1], C[2], C[3], C[4]]=[21, 0, 11, 2004] Corresponds to an elliptic curve of conductor 10988969958. To stimulate his already burgeoning mathematical talents.

The Mun Yau Group Set [C[1], C[2], C[3], C[4]]=[0,11, 0, 9] Corresponds to an elliptic curve of conductor 2040. From Elizabeth Lewis to celebrate the birthday of her daughter-in-law who is a maths graduate from York University.

The Sean 7 Birthday Group Set [C[1], C[2], C[3], C[4]]=[16,8, 0, 2001] Corresponds to an elliptic curve of conductor 90285120. For Sean White's seventh birthday from his grandparents. Sean has been a dedicated "groupie" of Finding Moonshine, having come already to two of my lectures and asking a very pertinent question about sporadic groups. Hope the Sean 7 Birthday Group spurs him on to great things.

The Miri Group Set [C[1], C[2], C[3], C[4]]=[0,18, 0, 8] Corresponds to an elliptic curve of conductor 4672. A present from Christoph Nowak for Miri's birthday.

The Grace K. Group Set [C[1], C[2], C[3], C[4]]=[127,0, 131, 137] Corresponds to an elliptic curve of conductor 601251522940274. A present from Lisa Black for Grace's 12th birthday.

The Samuel Kirkland Group Set [C[1], C[2], C[3], C[4]]=[10, 0, 11, 2003] Corresponds to an elliptic curve of conductor 103015407215. The Marcus Kirkland Group Set [C[1], C[2], C[3], C[4]]=[11, 10, 0, 2003] Corresponds to an elliptic curve of conductor 107617184. Twin groups for twins of Laura Lamont who spends her days latexing maths so probably understands what this is all about by now.

The Ryan Heaffey Group Set [C[1], C[2], C[3], C[4]]=[23, 0, 1, 1993] Corresponds to an elliptic curve of conductor 608925100798. A prize for Ryan who won a competition at the London Mathematics Summer School for showing strong promise at Mathematics and Mathematics Communication.

The Margaret Chambers Group Set [C[1], C[2], C[3], C[4]]=[139, 0, 149, 151] Corresponds to an elliptic curve of conductor 591420329470598. From Margaret's son Andrew.

The George Goodwin Group Set [C[1], C[2], C[3], C[4]]=[0, 30, 0, 10] Corresponds to an elliptic curve of conductor 137600. From Su Knight to her prospective father-in-law for his birthday.

The Robin Deeley Group Set [C[1], C[2], C[3], C[4]]=[31, 0, 1, 1980] Corresponds to an elliptic curve of conductor 396092524418. From Reyna Jenkyns to her math PhD student boyfriend who she met in the math department at the University of Waterloo.

The Christian Korninger Group Set [C[1], C[2], C[3], C[4]]=[157, 0, 163, 167] Corresponds to an elliptic curve of conductor 1313459491946782. From Leahanne Hobson.

The Martin Golumbic Group Set [C[1], C[2], C[3], C[4]]=[30, 0, 9, 1948] Corresponds to an elliptic curve of conductor 2924045005085. Mathematician and Algorithmic Graph Theorist.

The Samuel Eilenberg Group Set [C[1], C[2], C[3], C[4]]=[30, 0, 9, 1913] Corresponds to an elliptic curve of conductor 2835555384565. From Martin Golumbic for his thesis advisor, Samuel Eilenberg, Mathematician and Algebraic Topologist.

The Armstrong Group Set [C[1], C[2], C[3], C[4]]=[12, 0, 11, 0] Corresponds to an elliptic curve of conductor 15741. "For the best maths teacher a Queenie could wish for... Happy Birthday Mr Armstrong." From Jenny and Naomi.

The Scott Thomas Group Set [C[1], C[2], C[3], C[4]]=[11, 0, 12, 1968] Corresponds to an elliptic curve of conductor 1243262310. For my brother Scott Thomas who is 40 on 11th December this year and is obsessed with symmetry to almost OCD levels, the fool. From Marc Thomas.

The Sharoné Bentoné Group Set [C[1], C[2], C[3], C[4]]=[18, 0, 3, 1969] Corresponds to an elliptic curve of conductor 90679839931. From Tim: "Happy 40th Birthday".

The Abigail Pepperell Group Set [C[1], C[2], C[3], C[4]]=[173, 0, 179, 181] Corresponds to an elliptic curve of conductor 5074383987971138. From Geoff Savage. "My girlfriend is an English teacher who nearly became a science teacher and retains a strong fondness for the subject (she is still devoted to watching the Christmas lectures every year and passionately supports your belief in exposing children to complex ideas)."

The Stephen Ives Group Set [C[1], C[2], C[3], C[4]]=[19, 0, 6, 2009] Corresponds to an elliptic curve of conductor 8062834141. From Karen "to celebrate our 25th anniversary".

The Bentley Group Set [C[1], C[2], C[3], C[4]]=[40, 13, 4, 4] Corresponds to an elliptic curve of conductor 19135372. From Tony Mann: "A group to commemorate the wonderful goal scored by David Bentley last week from 40 yards in the 13th minute in the 4:4 draw between Spurs and Arsenal." This group certainly tested my commitment to the charity. As Tony knows, I am a big Arsenal fan. I was at the match and it was painful seeing Bentley's goal go in (Bentley is an ex-Arsenal who moved to Spurs and got booed all night). We thought we'd done enough at 4:2 with one minute of normal time to go. I've never heard the Emirates go so quiet after Spurs scored two last gasp goals to draw 4:4. Thank God for beating Man U. today. Tony, you are a cruel man!

The Matt Emanuele Group Set [C[1], C[2], C[3], C[4]]=[191, 0, 193, 197] Corresponds to an elliptic curve of conductor 9758279989066946. A Christmas present from Cliff Cunningham.

The Bas Kokshoorn Group Set [C[1], C[2], C[3], C[4]]=[199, 0, 211, 223] Corresponds to an elliptic curve of conductor 7412124287628142. A present from Ionica Smeets. "Bas Kokshoorn is a biologist and he named a snail after me, so this seemed the least I could do for him!"

The Dean David Group Set [C[1], C[2], C[3], C[4]]=[16, 0, 9, 1957] Corresponds to an elliptic curve of conductor 264377808699.

The Amy Baudains Group Set [C[1], C[2], C[3], C[4]]=[19, 0, 12, 2001] Corresponds to an elliptic curve of conductor 7418587161. From her Dad Ian. "As a very mediocre maths graduate, I may have some problems explaining to her precisely what it is, but I think it’s a great idea and something very special."

The Georgina Clark-Mazo Group Set [C[1], C[2], C[3], C[4]]=[227, 0, 229, 233] Corresponds to an elliptic curve of conductor 32425730045771918. A Christmas present from Georgina's husband Jeffrey.

The David Wheable Group Set [C[1], C[2], C[3], C[4]]=[28, 0, 2, 1989] Corresponds to an elliptic curve of conductor 1975062918032. From David's father John "My son David is in his second year reading Maths at Leeds. Hopefully he'll be able to explain it to me soon."

The Chloe Richmond Balfour Group Set [C[1], C[2], C[3], C[4]]=[13, 0, 4, 2004] Corresponds to an elliptic curve of conductor 26100675818. From Jason "for the date I met my wife."

The Wells-Mulligan Group Set [C[1], C[2], C[3], C[4]]=[239, 0, 241, 251] Corresponds to an elliptic curve of conductor 99724178588722. From Susan and Oliver Mulligan "a Christmas present for our daughter and son-in-law."

The Jessica Samuel Group Set [C[1], C[2], C[3], C[4]]=[257, 0, 263, 269] Corresponds to an elliptic curve of conductor 79905342249760922. From Julian to his daughter "who did not belive that such things can be done. "

The Julian Ransom Group Set [C[1], C[2], C[3], C[4]]=[2, 0, 12, 1964] Corresponds to an elliptic curve of conductor 7714154704. A symmetrical object to immortalize Mr Perfect, from a secret admirer.

The Lucy Corena Parkes Group Set [C[1], C[2], C[3], C[4]]=[30, 0, 9, 1975] Corresponds to an elliptic curve of conductor 2992995730853. A Christmas present from Lucy's husband Laurence.

The Kitty Bittersplit Group Set [C[1], C[2], C[3], C[4]]=[1, 1, 4, 4] Corresponds to an elliptic curve of conductor 1462. From Francis Potts.

The Ethan Duffell Group Set [C[1], C[2], C[3], C[4]]=[14, 0, 12, 1979] Corresponds to an elliptic curve of conductor 99412586764. A birthday present from Karen Reid.

The Justine Hartley Group Set [C[1], C[2], C[3], C[4]]=[8, 0, 8, -8] Corresponds to an elliptic curve of conductor 8288. "A symmetry group after the beautiful symmetry in my life Justine Hartley, my wife." The date encoded in the group is their wedding anniversary 8/8/1992 which Tom remembers as 8/8/-8. A true mathematician!

The Repussiahtnamas Group Set [C[1], C[2], C[3], C[4]]=[22, 21, 2, 6] Corresponds to an elliptic curve of conductor 17356628. "Sweet idea, dude! A group named for my girlie, Sammy." From Cam Ewens.

The Pip Group Set [C[1], C[2], C[3], C[4]]=[271, 0, 277, 281] Corresponds to an elliptic curve of conductor 114571909805857838. From Geoff Wright to his symmetrical palindromic brother Pip. "I intend to print T-shirts for the whole family to wear at XMAS containing the object, rotated on the front and inverted on the back, so a nice symmetry will be appreciated :-) " Might be a challenge printing an object in hyperspace on a t-shirt but at least you can print the equation at the top of the post which generates the object.

The Jonathan Camfield Group Set [C[1], C[2], C[3], C[4]]=[283, 0, 293, 307] Corresponds to an elliptic curve of conductor 10274520264457426. From Derek Camfield to his eldest son who studied maths at Cambridge and whose birthday is coming up soon. "Being from maths background myself (maths, economics and statistics at Birmingham), I am

particularly pleased that in your new position you may help to raise the status of maths to become

a cool subject to study."

The Tim Moore Group Set [C[1], C[2], C[3], C[4]]=[311, 0, 313, 317] Corresponds to an elliptic curve of conductor 290443732551869066. From Derek Camfield to Tim for his 17th birthday. "He’s studying maths at A-level and, with his family,

is also a Dr Who fan. He and his parents really appreciated the present of a

symmetrical object in hyperspace – it seems very Dr Who-ish."

The Ashley Carter Group Set [C[1], C[2], C[3], C[4]]=[11, 0, 1, 1972] Corresponds to an elliptic curve of conductor 218828042458. From Morgan Parker for Ashley's birthday.

The Phung Luu Group Set [C[1], C[2], C[3], C[4]]=[331, 0, 337, 347] Corresponds to an elliptic curve of conductor 29207729268459674. From David Plevin.

The David Pickup Group Set [C[1], C[2], C[3], C[4]]=[349, 0, 353, 359] Corresponds to an elliptic curve of conductor 329878042828105666. "For our son david who is studying maths/phys at warwick university."

The Crackhouseceilidhband Group Set [C[1], C[2], C[3], C[4]]=[367, 0, 373, 379] Corresponds to an elliptic curve of conductor 118268480847339994. Named by Iain Brassington.

The Kim Lasscock Group Set [C[1], C[2], C[3], C[4]]=[383, 0, 389, 397] Corresponds to an elliptic curve of conductor 1279154466551486474. From Kim's daughter Sara. "Merry Christmas Gap "

The David Hurn Group Set [C[1], C[2], C[3], C[4]]=[0, 27, 0, 12] Corresponds to an elliptic curve of conductor 32688. From David's son Mark for his birthday.

The Jessica Goodman Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 0, 31415926] Corresponds to an elliptic curve of conductor 63165466011998464. From Simon and Emily who were keen to cook pi into the symmetry.

The Noodle Group Set [C[1], C[2], C[3], C[4]]=[401, 0, 409, 419] Corresponds to an elliptic curve of conductor 446373494996309666. From a Pieceofstring to his wife Noodle.

The b4thebigbang Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 0, 13700000000] Corresponds to an elliptic curve of conductor 1201216. Named by Peter Cohen who wanted a symmetrical object that relates to the shape of empty space.

The Ricci & Spinne Group Set [C[1], C[2], C[3], C[4]]=[27, 0, 5, 2009] Corresponds to an elliptic curve of conductor 1716726955870. For Mr. & Mrs. Ricci & Spinne Downard's 20th Wedding Anniversary on 27 May 2009.

The Wimmett Group Set [C[1], C[2], C[3], C[4]]=[258, 301, 344, 384] Corresponds to an elliptic curve of conductor 88535365183360. From Stewart Robertson for his perfectly symetrical wife this Christmas. The group has encoded in it some character degrees of SU_3(7). "My maths is very rusty, but about 30 years ago I tinkered briefly with Lie Groups and Lie Algebras, looking at the symmetries of elementary particles, so anything related to SU(3) would be particularly appreciated! Thanks for the great books & TV, and what you're doing to fight poverty!"

The Tessa Keytes Markham Group Set [C[1], C[2], C[3], C[4]]=[8, 0, 11, 1998] Corresponds to an elliptic curve of conductor 527582450987. From Adam and Vicky Markham to their daughter who at 10 is a mathematician in the making. "This brilliant idea of yours – which I read about in New Scientist – may help continue to grow her interest in both maths and philanthropy. If you can get her group up on your blog by Christmas that would be great – who doesn’t want their very own elliptic curve under the tree!"

The Calum MacLeod Group Set [C[1], C[2], C[3], C[4]]=[421, 0, 431, 433] Corresponds to an elliptic curve of conductor 2479605410685210214. From Kenny to his Dad who has just retired from teaching Maths after 40-odd years. "He's never lost his sense of enthusiasm and curiosity about the subject, which I think is remarkable after teaching countless hundreds of reluctant students."

The Miners Hochheimer Kirkman Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 0, 2003] Corresponds to an elliptic curve of conductor 128384288. Named by James Miners whose generous donation took funds raised for Common Hope to the first prime after 2000.

The Alexander James Heggie Group Set [C[1], C[2], C[3], C[4]]=[10, 0, 12, 1943] Corresponds to an elliptic curve of conductor 37896380. From Vanessa to celebrate her father's 65th birthday.

The Yakov Group Set [C[1], C[2], C[3], C[4]]=[439, 0, 443, 449] Corresponds to an elliptic curve of conductor 296138264886917662. From Su Chiang to her husband.

The Evangeline Group Set [C[1], C[2], C[3], C[4]]=[457, 0, 461, 463] Corresponds to an elliptic curve of conductor 2136360038099416790. From Su Chiang to her cousin.

The Peter Christopher Carroll Group Set [C[1], C[2], C[3], C[4]]=[57, 0, 40, 58] Corresponds to an elliptic curve of conductor 716712588058. Named by Aoife Fitzpatrick for her wonderful husband. "Thank you for the opportunity to donate, and for the opportunity to pass on such an interesting, philosphically challenging, beautiful

and, actually, quite moving gift."

The Wandja Group Set [C[1], C[2], C[3], C[4]]=[467, 0, 479, 487] Corresponds to an elliptic curve of conductor 2601578536477673458. Named by Carol Poole. Merry Christmas.

The Catrin Lewis Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 0, 4.1x10^586] Corresponds to an elliptic curve of conductor 10758400. Named by Andrew Langworthy for his gorgeous girlfriend for Christmas. One can only speculate at the significance of such a large number in their relationship.

The Judith Rolfe Group Set [C[1], C[2], C[3], C[4]]=[12, 0, 9, 1958] Corresponds to an elliptic curve of conductor 436967312507. Named by Rob Rolfe for his wife.

The Alan Williamson Group Set [C[1], C[2], C[3], C[4]]=[25, 0, 7, 1949] Corresponds to an elliptic curve of conductor 1077636797162. A present from Secret Santa who says that you of all people with your PhD in group theory should understand what this group is all about.

The Jenny Danczak Group Set [C[1], C[2], C[3], C[4]]=[491, 0, 499, 503] Corresponds to an elliptic curve of conductor 3595593229000931302. Named by Julian Dickens.

The Felix Danczak Group Set [C[1], C[2], C[3], C[4]]=[509, 0, 521, 523] Corresponds to an elliptic curve of conductor 2336359840205816966. Named by Julian Dickens.

The Fran Danczak Group Set [C[1], C[2], C[3], C[4]]=[541, 0, 547, 557] Corresponds to an elliptic curve of conductor 14170826984968211114. Named by Julian Dickens.

The Leo Danczak Group Set [C[1], C[2], C[3], C[4]]=[563, 0, 569, 571] Corresponds to an elliptic curve of conductor 1152595426554951278. Named by Julian Dickens.

The Dan Salter Group Set [C[1], C[2], C[3], C[4]]=[919, 0, 929, 937] Corresponds to an elliptic curve of conductor 571829388597171645214. Named by Cherry Lewis. "A great idea for Xmas presents, and a nice change from the Oxfam goats and chickens!"

The Leon Salter Group Set [C[1], C[2], C[3], C[4]]=[941, 0, 947, 953] Corresponds to an elliptic curve of conductor 667269326466624957470. Named by Cherry Lewis.

The Jo Smyth Group Set [C[1], C[2], C[3], C[4]]=[967, 0, 971, 977] Corresponds to an elliptic curve of conductor 803769097553289303194. Named by Cherry Lewis.

The Teresa Gray Group Set [C[1], C[2], C[3], C[4]]=[983, 0, 991, 997] Corresponds to an elliptic curve of conductor 908676036071455805326. Named by Cherry Lewis.

The Chris Smyth Group Set [C[1], C[2], C[3], C[4]]=[1009, 0, 1013, 1019] Corresponds to an elliptic curve of conductor 270413451369674373158. Named by Cherry Lewis for a number theorist in Edinburgh who can explain what's going on to the rest of Cherry's clan.

The Banda Group Set [C[1], C[2], C[3], C[4]]=[577, 0, 587, 593] Corresponds to an elliptic curve of conductor 22338170231254069814. Named by Ruben Flores, a Mexican PhD

candidate in Sociology at the University of Kent interested in contributing to development in Latin America.

The Tia Eustolita Group Set [C[1], C[2], C[3], C[4]]=[599, 0, 601, 607] Corresponds to an elliptic curve of conductor 14111748419094544178. Named by Ruben Flores, a Mexican PhD

candidate in Sociology at the University of Kent interested in contributing to development in Latin America.

The Rory Browne Group Set [C[1], C[2], C[3], C[4]]=[613, 0, 617, 619] Corresponds to an elliptic curve of conductor 8290914111359460658. Named by Tony Mann. Happy Christmas.

The Calum Browne Group Set [C[1], C[2], C[3], C[4]]=[631, 0, 641, 643] Corresponds to an elliptic curve of conductor 2584923289182691174. Named by Tony Mann. Happy Christmas.

The Andreas Mann Group Set [C[1], C[2], C[3], C[4]]=[647, 0, 653, 659] Corresponds to an elliptic curve of conductor 12234186943678509998. Named by Tony Mann. Happy Christmas.

The Niklas Mann Group Set [C[1], C[2], C[3], C[4]]=[661, 0, 673, 677] Corresponds to an elliptic curve of conductor 57663962798415443726. Named by Tony Mann. Happy Christmas.

The Katie Reid Group Set [C[1], C[2], C[3], C[4]]=[683, 0, 691, 701] Corresponds to an elliptic curve of conductor 72201888470849537942. Named by Tony Mann. Happy Christmas.

The Joanna Reid Group Set [C[1], C[2], C[3], C[4]]=[709, 0, 719, 727] Corresponds to an elliptic curve of conductor 46953727861032288482. Named by Tony Mann. Happy Christmas.

The Eilidh Reid Group Set [C[1], C[2], C[3], C[4]]=[733, 0, 739, 743] Corresponds to an elliptic curve of conductor 58248775917005188990. Named by Tony Mann. Happy Christmas.

The Dawn Pfeil Group Set [C[1], C[2], C[3], C[4]]=[751, 0, 757, 761] Corresponds to an elliptic curve of conductor 137980116991018190798. Named by Tony Mann. Happy Christmas.

The Matthew Kippen Group Set [C[1], C[2], C[3], C[4]]=[769, 0, 773, 787] Corresponds to an elliptic curve of conductor 20502405894074885378. From Sarah Langford to her brother.

The Stephen Poyer Group Set [C[1], C[2], C[3], C[4]]=[797, 0, 809, 811] Corresponds to an elliptic curve of conductor 52878209484444161198. From Chris Grollman to Stephen Poyer, "who looks so like me that we are often confused." So a bit of symmetry seems appropriate.

The Noah Slater Group Set [C[1], C[2], C[3], C[4]]=[5, 0, 2, 1983] Corresponds to an elliptic curve of conductor 500365533065. Named by Alison Wilde.

The Nerida Dicko Group Set [C[1], C[2], C[3], C[4]]=[821, 0, 823, 827] Corresponds to an elliptic curve of conductor 31810440742807494622. A Christmas present from Gareth Dickinson "to my fantastic wife!"

The David Woolf Group Set [C[1], C[2], C[3], C[4]]=[829, 0, 839, 853] Corresponds to an elliptic curve of conductor 280877690224362556594. A Christmas present to a man whose first love was Physics and growing crystals/semiconductors but now aspires to be a Time Lord. From his wife Alison and daughter Ellen. "Such a great idea, especially when looking for a present for the "man who has everything" - said man has declared he doesn't want a present this year and suggested, perhaps not entirely seriously, that a goat could go on his behalf to the Third World. I think he'll like this better."

The Kevlin Henney Group Set [C[1], C[2], C[3], C[4]]=[857, 0, 859, 863] Corresponds to an elliptic curve of conductor 171740916276470528254. Some symmetry from Carolyn Morris to her husband "so for once I am giving him order instead of chaos." [If you send me your email I'll send you a certificate]

The Anni Uibu Group Set [C[1], C[2], C[3], C[4]]=[877, 0, 881, 883] Corresponds to an elliptic curve of conductor 50561397167771465030. From Mari Järve to a fellow mathematician.

The Graham Perkins Group Set [C[1], C[2], C[3], C[4]]=[887, 0, 907, 911] Corresponds to an elliptic curve of conductor 227345263670881519582. A Christmas present from Andrew to his brother.

The Madeleine Shepherd Group Set [C[1], C[2], C[3], C[4]]=[1021, 0, 1031, 1033] Corresponds to an elliptic curve of conductor 1183938363633519730414. A Christmas present from Scott Keir with best wishes for 2009.

The Evatt Bourne Group Set [C[1], C[2], C[3], C[4]]=[1039, 0, 1049, 1051] Corresponds to an elliptic curve of conductor 334366632813643462474. Named by Jade Suine for Evatt, "who has become very excited by the things he has been reading about you and your work." For a wonderful 2009.

The Marjorie Marks Group Set [C[1], C[2], C[3], C[4]]=[1061, 0, 1063, 1069] Corresponds to an elliptic curve of conductor 1530717085799808534394. Named by Melissa Young for Marjorie Marks "who is a great College Algebra teacher & is very cool. Thank you for having a place where I can combine my interest in math, community outreach, and learning."

The Kristen Harley Group Set [C[1], C[2], C[3], C[4]]=[4, 0, 4, 1988] Corresponds to an elliptic curve of conductor 15872033048. For Kristen's 21st birthday from her parents. "Kristen is in her fourth year of a Maths/Physics degree at QUT (Queensland University of Technology) here in Brisbane, Australia. Perhaps it was inevitable she'd have a passion for maths, when she was born on 4/4/88."

The Paul Simon David Group Set [C[1], C[2], C[3], C[4]]=[17, 0, 12, 1960] Corresponds to an elliptic curve of conductor 4277374566. Named by Dean David in memory of Paul Simon David.

The Jermaine Defoe Group Set [C[1], C[2], C[3], C[4]]=[7, 0, 1, 15000000] Corresponds to an elliptic curve of conductor 107999805487384972499842. Named by Tony Mann for "the star who will make Spurs the best team in north London." That's TWO Tottenham players Tony has immortalised in hyper-space. Where are all you Gooners? Help me in the fight back against our arch-rivals at White Hart Lane. Surely Fabregas deserves a symmetrical object named after him after all the triangles he threads on the pitch?

The Kai Kuehner Group Set [C[1], C[2], C[3], C[4]]=[27, 0, 1, 2009] Corresponds to an elliptic curve of conductor 1644317287102. Named by Kai's grandparent's for Kai's birthday.

The Ameli Gottstein Group Set [C[1], C[2], C[3], C[4]]=[25, 0, 12, 2008] Corresponds to an elliptic curve of conductor 8129515890. Ameli's prize for winning the Greenwich University Christmas Maths Quiz. She preferred that to an Amazon token - clearly a mathematician in the making.

The Marta Kupis Group Set [C[1], C[2], C[3], C[4]]=[17, 0, 1, 1984] Corresponds to an elliptic curve of conductor 15879470398. For Marta's 25th birthday from Frank Neumann.

The Craig Gallagher Group Set [C[1], C[2], C[3], C[4]]=[21, 0, 1, 2009] Corresponds to an elliptic curve of conductor 266039568082. Named by Darshini Gallagher for her father's birthday, "the loveliest geek in the world!"

The Joel Ineson Group Set [C[1], C[2], C[3], C[4]]=[14, 0, 2, 1968] Corresponds to an elliptic curve of conductor 86842276988. A birthday and Valentine's day present with love as always from Rachel.

The Mark and Susan Oeltjenbruns Group Set [C[1], C[2], C[3], C[4]]=[4, 5, 15, 1996] Corresponds to an elliptic curve of conductor 526617649243 A group is in celebration of Mark and Susan's wedding anniversary and their five wonderful kids.

The Tim Camfield Group Set [C[1], C[2], C[3], C[4]]=[0, 15, 0, 2009] Corresponds to an elliptic curve of conductor 17934056. A group is in celebration of Tim's 15th birthday.

The Harald Bohr Group Set [C[1], C[2], C[3], C[4]]=[22, 0, 4, 1887] Corresponds to an elliptic curve of conductor 103121269204. Named by Simon Singh for Harald Bohr, mathematician and footballer, born on 22 April 1887. Harald's brother, Niels, was ultimately to become more famous as one of the creators of the theory of quantum physics. Harald himself had already carved out some notoriety having been a key player in Denmark's Olympic football team that secured silver at the 1908 Olympics. But his greatest contributions were in studying the zeros of the Riemann zeta function. You can find out more about his discoveries in Chapter 5 of The Music of the Primes.

The Dong-ke Zhang Group Set [C[1], C[2], C[3], C[4]]=[8, 0, 3, 1964] Corresponds to an elliptic curve of conductor 477775260811. A present from David for his father "who first taught me the wonders of mathematics. Happy Birthday."

The Pauline "Popsie" Byron Group Set [C[1], C[2], C[3], C[4]]=[22, 0, 4, 1943] Corresponds to an elliptic curve of conductor 105656241812. A present from Olwyn for her mother for her birthday.

The Doris Whitworth Group Set [C[1], C[2], C[3], C[4]]=[10, 0, 8, 1929] Corresponds to an elliptic curve of conductor 449578789168. From Geoffrey Morley in memory of his first cousin who died on the 31st of March.

The Andrew Plater Group Set [C[1], C[2], C[3], C[4]]=[1087, 0, 1091, 1093] Corresponds to an elliptic curve of conductor 1812931295453793579070. From David Hunt in memory of Dr Andrew Plater, a man who touched the hearts and minds of many.

The Georgina Knight Group Set [C[1], C[2], C[3], C[4]]=[11, 0, 8, 1991] Corresponds to an elliptic curve of conductor 478466261623. From Chris Buckley "for my wonderful girlfriend".

The Jansson Group Set [C[1], C[2], C[3], C[4]]=[1097 0 1103 1109] Corresponds to an elliptic curve of conductor 1946805281289695949842. Named by Torbjörn Jansson for his family.

The Dahlström Group Set [C[1], C[2], C[3], C[4]]=[1117 0 1123 1129] Corresponds to an elliptic curve of conductor 2208554106995230334702. Named by Magnus Dahlström. "I enjoyed your lecture in Gothenburg."

The Ben Moore Group Set [C[1], C[2], C[3], C[4]]=[1131 0 1137 1149] Corresponds to an elliptic curve of conductor 807293329303094999694. Named by Derek Camfield for Ben on his 15 Birthday. "Keep up the good work in science!"

The Anna Shimwell Group Set [C[1], C[2], C[3], C[4]]=[28 0 5 1996] Corresponds to an elliptic curve of conductor 2056908575317. Named by John Shimwell for his daughter on her Birthday.

The Lena Jansson Group Set [C[1], C[2], C[3], C[4]]=[26 0 6 1959] Corresponds to an elliptic curve of conductor 75184952064. Named by Torbjörn Jansson for his sister-in-law to celebrate her 50th birthday.

The Dave Edwards Group Set [C[1], C[2], C[3], C[4]]=[20, 0, 6, 2009] Corresponds to an elliptic curve of conductor 118040761232. Named by Linda Higginbottom: "For my science and book buddy to celebrate his birthday.

The Sophia Group Set [C[1], C[2], C[3], C[4]]=[29, 0, 9, 2009] Corresponds to an elliptic curve of conductor 2601346244402. "For my sunshine Sophia for our anniversary ".

The Lasse Johansson Group Set [C[1], C[2], C[3], C[4]]=[1151, 0, 1153, 1163] Corresponds to an elliptic curve of conductor 678375945011528041802. From Torbjörn, Birgitta, Roland, Ann-Louise.

The Suzanne Stonehouse Group Set [C[1], C[2], C[3], C[4]]=[3, 0, 8, 1965] Corresponds to an elliptic curve of conductor 54911265687. From Alec Stonehouse to his wife for her birthday: "A trailblazing secondary school Maths teacher & Symmetry fan." [August '65...a very good vintage]

The Rolf Nyberg Group Set [C[1], C[2], C[3], C[4]]=[1, 0, 9, 2009] Corresponds to an elliptic curve of conductor 522431328766. From Torbjörn Jansson for his friend and colleague in recognition of his retirement.

The Torbjörn Jansson Group Set [C[1], C[2], C[3], C[4]]=[1171 0 1181 1187] Corresponds to an elliptic curve of conductor 386482449719183404618. For Torbjörn Jansson. Many thanks for all your support with my project.

The Cathy and Greg Group Set [C[1], C[2], C[3], C[4]]=[3, 0, 9, 2009] Corresponds to an elliptic curve of conductor 529117450658. From the Staff and Students of CSI Dublin to mark Cathy and Greg's wedding anniversary.

The Stefan Ottmar Haug Group Set [C[1], C[2], C[3], C[4]]=[4, 0, 9, 2009] Corresponds to an elliptic curve of conductor 531918335323. From Benjamin Volk and Panagiotis Konstantis for Stefan Ottmar Haug's birthday.

The Tordoff Group Set [C[1], C[2], C[3], C[4]]=[1193 0 1201 1213] Corresponds to an elliptic curve of conductor 3526360473742239108358. From Thomas Walton for Rachel who organised our trip to the Emirates achievement.

The Arnau Rios Huguet Group Set [C[1], C[2], C[3], C[4]]=[15, 0, 10, 1980] Corresponds to an elliptic curve of conductor 266464350. From Flor, Maria, Nacho and Yago "for our friend Arnau Rios Huguet to celebrate his 2^2+3^2+4^2 birthday."

The Venexia Group Set [C[1], C[2], C[3], C[4]]=[1217 0 1223 1229] Corresponds to an elliptic curve of conductor 4019178174064472055002. From David Walker for his daughter.

The PALYAB Group Set [C[1], C[2], C[3], C[4]]=[1231 0 1237 1249] Corresponds to an elliptic curve of conductor 4374420264075456706982. Named by Abby Pace.

The TJ Group Set [C[1], C[2], C[3], C[4]]=[22 0 7 1992] Corresponds to an elliptic curve of conductor 435446962861. Named by Tim Ladd for a young man with Leukemia in MI. Check out his website at tjsjourney.com or his mom's youtube channel: *http://www.youtube.com/user/WackaDoodleFreeZone

The Dadhaniya Group Set [C[1], C[2], C[3], C[4]]=[1259 0 1277 1279] Corresponds to an elliptic curve of conductor 2587295415673917568522. Named by Darpan Dadhaniya for his family.

The Mozz Group Set [C[1], C[2], C[3], C[4]]=[16 0 10 2009] Corresponds to an elliptic curve of conductor 296901944560. From Billy Boyle to celebrate Mozz's birthday.

The Jarrod Tanton Group Set [C[1], C[2], C[3], C[4]]=[22 0 12 1987] Corresponds to an elliptic curve of conductor 4087829532. From Zachary Tanton "for my cousin who with his vastly superior mathematical knowledge would be very intrigued."

The John and Jana Hoffman Group Set [C[1], C[2], C[3], C[4]]=[1283 0 1289 1291] Corresponds to an elliptic curve of conductor 724256730128301773266. Named by Irene Hoffman for her beloved parents.

The georgeNgeorge Group Set [C[1], C[2], C[3], C[4]]=[1297 0 1301 1303] Corresponds to an elliptic curve of conductor 623137684751104311490. Named by Klupu.

The Martens Group Set [C[1], C[2], C[3], C[4]]=[1307 0 1319 1321] Corresponds to an elliptic curve of conductor 6655565208577887603842. Named by Joel Martens. "I saw your TED Talks video on youtube and was fascinated. Your idea to raise money by naming mathematical objects is brilliant. I am an undergrad student studying mathematics and physics and i'd love to get some details on the properties, behavior and origins of the object that you end up naming for me. Im going to start by getting your book but i'd really appreciate any additional specifics you could send me. Thanks again for such a brilliant initiative."

The Stephanie Simon Group Set [C[1], C[2], C[3], C[4]]=[1327 0 1361 1367] Corresponds to an elliptic curve of conductor 3833593484133661049542. Named by Jonathan Joyce.

The Neville Neill Group Set [C[1], C[2], C[3], C[4]]=[20 0 7 1978] Corresponds to an elliptic curve of conductor 433344982589. Named by Jackie Neill to mark the day she married Neville.

The Doozer Group Set [C[1], C[2], C[3], C[4]]=[19 0 10 2009] Corresponds to an elliptic curve of conductor 18999485185. Named by Michelle Robert for her financée to mark their engagement.

The Awesome Allsworth Group Set [C[1], C[2], C[3], C[4]]=[21 0 10 2009] Corresponds to an elliptic curve of conductor 264031198435. To celebrate "the epic US install trip" 21st Oct 2009 from Owlstone.

The Elizabeth Davies Group Set [C[1], C[2], C[3], C[4]]=[25 2 12 2009] Corresponds to an elliptic curve of conductor 1218057747373. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Russell Collins Group Set [C[1], C[2], C[3], C[4]]=[25 3 12 2009] Corresponds to an elliptic curve of conductor 1241585245589. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Trevor Addenbrooke Group Set [C[1], C[2], C[3], C[4]]=[25 5 12 2009] Corresponds to an elliptic curve of conductor 1289081106757. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Julie Newton Group Set [C[1], C[2], C[3], C[4]]=[25 7 12 2009] Corresponds to an elliptic curve of conductor 1337164695413. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Patricia O'Rorke Group Set [C[1], C[2], C[3], C[4]]=[25 11 12 2009] Corresponds to an elliptic curve of conductor 1435094612821. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Phil Peel Group Set [C[1], C[2], C[3], C[4]]=[25 13 12 2009] Corresponds to an elliptic curve of conductor 1484940720389. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Lucy Hibbert Group Set [C[1], C[2], C[3], C[4]]=[25 17 12 2009] Corresponds to an elliptic curve of conductor 1586394680293. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Ben Ponniah Group Set [C[1], C[2], C[3], C[4]]=[25 19 12 2009] Corresponds to an elliptic curve of conductor 1638002311445. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Ian Gordon-Brown Group Set [C[1], C[2], C[3], C[4]]=[25 23 12 2009] Corresponds to an elliptic curve of conductor 1742978323189. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Michael Ingham Group Set [C[1], C[2], C[3], C[4]]=[25 29 12 2009] Corresponds to an elliptic curve of conductor 2254251545. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Greg Kerr Group Set [C[1], C[2], C[3], C[4]]=[25 31 12 2009] Corresponds to an elliptic curve of conductor 1959970247861. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The Allan Westman Group Set [C[1], C[2], C[3], C[4]]=[25 37 12 2009] Corresponds to an elliptic curve of conductor 2128870621253. A Christmas gift to say thank you for all your hard work, dedication, enthusiasm and support at School from Michelle Roberts.

The James Graef Group Set [C[1], C[2], C[3], C[4]]=[1373 0 1381 1399] Corresponds to an elliptic curve of conductor 4720208163786201526262. Named by Edward McCoy.

The Kim Sundermann Group Set [C[1], C[2], C[3], C[4]]=[1 0 11 2009] Corresponds to an elliptic curve of conductor 523208880658.

The Greg Conklin Group Set [C[1], C[2], C[3], C[4]]=[1409 0 1423 1427] Corresponds to an elliptic curve of conductor 176447821050061918346. Named by Brian Quistorff.

The Aparicio Group Set [C[1], C[2], C[3], C[4]]=[1429 0 1433 1439] Corresponds to an elliptic curve of conductor 6152335086016734640366. Named by Jose Aparicio. "I have to say that I really appreciate your efforts, and think this is a most wonderful way to use your craft to raise money to help in the advancement of mathematical education. Cheers!"

The Nick Sweeting Group Set [C[1], C[2], C[3], C[4]]=[1447 0 1451 1453] Corresponds to an elliptic curve of conductor 2678552181868463134670. From Tania+Frank+Corey for Nick's 13th birthday.

The Berheide Group Set [C[1], C[2], C[3], C[4]]=[1459 0 1471 1481] Corresponds to an elliptic curve of conductor 14422328284176205274114.

The Magiel Harmse Group Set [C[1], C[2], C[3], C[4]]=[11 0 7 2009] Corresponds to an elliptic curve of conductor 9954646702. Named by Attie Harmse for her brother's birthday.

The Igal Levine Group Set [C[1], C[2], C[3], C[4]]=[1483 0 1487 1489] Corresponds to an elliptic curve of conductor 2271922558380688700326. "Thank you for this unique opportunity to give a special gift and at the same time contribute to a very good cause."

The Moni Group Set [C[1], C[2], C[3], C[4]]=[1493 0 1499 1511] Corresponds to an elliptic curve of conductor 8412243298709054785774. "I just watched your TED talk and greatly enjoyed it. I especially love your fundraising idea. My first time living, working, and volunteering abroad was in Guatemala, it's a really special place and I'm excited to see that you're helping out there." Thanks for the symmetrical donation of 33.33. It took my fundraising over $4000.

The Niarte Group Set [C[1], C[2], C[3], C[4]]=[12 0 11 2009] Corresponds to an elliptic curve of conductor 481945494923. For Niarte's birthday. "a nerdy idea, with a rather warm hearty background. Bravo. :-)"

The Sethi Group Set [C[1], C[2], C[3], C[4]]=[1523 0 1531 1543] Corresponds to an elliptic curve of conductor 9691174762659229308974. Named by Nikhil Sethi.

The Lassonde Group Set [C[1], C[2], C[3], C[4]]=[7 0 9 2009] Corresponds to an elliptic curve of conductor 533597989426. Named by Nate Derbinsky.

The Charco Group Set [C[1], C[2], C[3], C[4]]=[23 0 11 1982] Corresponds to an elliptic curve of conductor 40133119646. For Charco's birthday.

The Elliot C Wilson Group Set [C[1], C[2], C[3], C[4]]=[12 0 7 1983] Corresponds to an elliptic curve of conductor 148729963977. For Elliot's birthday.

The Lovely Emma Group Set [C[1], C[2], C[3], C[4]]=[22 0 7 1973] Corresponds to an elliptic curve of conductor 432578991749. Named by Andy Low for Emma's birthday.

The Teacher I Is Group Set [C[1], C[2], C[3], C[4]]=[1583 0 1597 1601] Corresponds to an elliptic curve of conductor 25447571350049764792166. Named by Andrew Hirst for his family. "I named the group "Teacher I Is" partly due to my profession but also because it is an anagram containing all of my families initials."

The Nick Buzatu Group Set [C[1], C[2], C[3], C[4]]=[1549 0 1553 1559] Corresponds to an elliptic curve of conductor 10809368363512852108666. Named by Daniel Buzatu.

The Alex Buzatu Group Set [C[1], C[2], C[3], C[4]]=[1567 0 1571 1579] Corresponds to an elliptic curve of conductor 5866683193921799919238. Named by Daniel Buzatu.

The istemfer Group Set [C[1], C[2], C[3], C[4]]=[16 0 11 2009] Corresponds to an elliptic curve of conductor 301317556843. Named by Uygar Polat.

The Gomez Paez Group Set [C[1], C[2], C[3], C[4]]=[8 0 12 1968] Corresponds to an elliptic curve of conductor 2642786148. Named by Tim Sheehy.

The Anna Blume Group Set [C[1], C[2], C[3], C[4]]=[2 11 2009 3924944911] Corresponds to an elliptic curve of conductor 429970662482840185163704716195. Named by Jonathan Joyce to mark the publication of a collection of poetry by Anna Blume published November 2 on the subject of the Berlin Wall: West + Ost = Deutsch (ISBN: 3924944911). "An interesting (a)symmetry if ever I saw one.."

The uygarpolat Group Set [C[1], C[2], C[3], C[4]]=[11 0 16 2009] Corresponds to an elliptic curve of conductor 524730931183. Named by Istem Fer for her boyfriend. "Thank you for your being sensible for the children in Guetamala, I really appreciate that."

The Norman and Wendy Kay Group Set [C[1], C[2], C[3], C[4]]=[1583 0 1597 1601] Corresponds to an elliptic curve of conductor 25447571350049764792166. Named by Jeremy Levine for his wife's amazing parents.

The Verity Robertson Group Set [C[1], C[2], C[3], C[4]]=[6 0 11 2009] Corresponds to an elliptic curve of conductor 41490446231. Named by Calum Robertson for his daughter "so that she doesn't get jealous of her brother Rowan's group!"

The Vince Ion Group Set [C[1], C[2], C[3], C[4]]=[13 0 10 1950] Corresponds to an elliptic curve of conductor 4071505070. Named by Danny Ion for his Dad.

The Thomas Epping Group Set [C[1], C[2], C[3], C[4]]=[1607 0 1609 1613] Corresponds to an elliptic curve of conductor 27848720171084562011258. Named by Saskia Kersten.

The Lowe Group Set [C[1], C[2], C[3], C[4]]=[18 0 11 2009] Corresponds to an elliptic curve of conductor 132567234011. Named by Torbjörn and Birgitta Jansson for their first grandchild.

The Jules DesJacques Group Set [C[1], C[2], C[3], C[4]]=[1619 0 1621 1627] Corresponds to an elliptic curve of conductor 7343047481438450220754. Named by Aline Dutruel "my wee cousin Jules DesJacques, who's mad about mathematics, and will be thrilled with his Christmas present!"

The Charles Tyler Rives Group Set [C[1], C[2], C[3], C[4]]=[1637 0 1657 1663] Corresponds to an elliptic curve of conductor 16216485370370651836142.

The Bri and Jason Bird Group Set [C[1], C[2], C[3], C[4]]=[1667 0 1669 1693] Corresponds to an elliptic curve of conductor 36417295608366083835898.

The Kevin Moon Group Set [C[1], C[2], C[3], C[4]]=[1697 0 1699 1709] Corresponds to an elliptic curve of conductor 40912117957088347054634. Named by Peter and Susanne.

The Nicole Newman Group Set [C[1], C[2], C[3], C[4]]=[7 0 11 2009] Corresponds to an elliptic curve of conductor 539073092638. Named by Jeff Newman.

The Ryan McDonald Group Set [C[1], C[2], C[3], C[4]]=[1721 0 1723 1733] Corresponds to an elliptic curve of conductor 45132406297277785685618.

The Sean McDonald Group Set [C[1], C[2], C[3], C[4]]=[1723 0 1733 1721] Corresponds to an elliptic curve of conductor 45342629941969349921534.

The Kyle McDonald Group Set [C[1], C[2], C[3], C[4]]=[1733 0 1721 1723] Corresponds to an elliptic curve of conductor 11600957669426085848222.

The Young Group Set [C[1], C[2], C[3], C[4]]=[1741 0 1747 1753] Corresponds to an elliptic curve of conductor 49041509901414143107070.

The Gerry Callaghan Group Set [C[1], C[2], C[3], C[4]]=[1759 0 1777 1783] Corresponds to an elliptic curve of conductor 26707285435472064591334. Named by Sarah Callaghan for her Dad.

The Madeleine Leidheiser Group Set [C[1], C[2], C[3], C[4]]=[8 0 7 1985] Corresponds to an elliptic curve of conductor 505340998651. Named by Nils Blass.

The Elke Group Set [C[1], C[2], C[3], C[4]]=[1787 0 1789 1801] Corresponds to an elliptic curve of conductor 58779893562687073577422.

The Emma Group Set [C[1], C[2], C[3], C[4]]=[29 0 10 1968] Corresponds to an elliptic curve of conductor 635598612014. Named by Patrick.

The Kiwiokie Group Set [C[1], C[2], C[3], C[4]]=[1811 0 1823 1831] Corresponds to an elliptic curve of conductor 32547242821662244941586. Named by Shaun.

The Billy Sample Group Set [C[1], C[2], C[3], C[4]]=[12 0 0 2008] Corresponds to an elliptic curve of conductor 13525888.

The Dianne Group Set [C[1], C[2], C[3], C[4]]=[1847 0 1861 1867] Corresponds to an elliptic curve of conductor 9345512474654393927438. Named by Davin.

The Rola Al-Hammoud Group Set [C[1], C[2], C[3], C[4]]=[3 3 3 2009] Corresponds to an elliptic curve of conductor 520643420189.

The Implex Group Set [C[1], C[2], C[3], C[4]]=[1871 0 1873 1877] Corresponds to an elliptic curve of conductor 80692188750802744959026. Named by Meredith.

The Garrod Musto Group Set [C[1], C[2], C[3], C[4]]=[16 0 2 2009] Corresponds to an elliptic curve of conductor 262681892848. Named by Garrod's children for his Christmas present.

The Garry Musto Group Set [C[1], C[2], C[3], C[4]]=[10 10 10 10] Corresponds to an elliptic curve of conductor 298600. Named by Garrod for an inspirational father.

The Bencsics Group Set [C[1], C[2], C[3], C[4]]=[12 0 3 87] Corresponds to an elliptic curve of conductor 50085063.

The LEDERMAN Group Set [C[1], C[2], C[3], C[4]]=[1879 0 1889 1901] Corresponds to an elliptic curve of conductor 84199111164843313025306.

The Tamp Lawrence Group Set [C[1], C[2], C[3], C[4]]=[21 0 7 1977] Corresponds to an elliptic curve of conductor 265680465534.

The James Dickson Group Set [C[1], C[2], C[3], C[4]]=[20 0 2 1965] Corresponds to an elliptic curve of conductor 129862983568. Named by Emma Dickson.

The Gwyneth Vaughan Lamboll Group Set [C[1], C[2], C[3], C[4]]=[1907 0 1913 1931] Corresponds to an elliptic curve of conductor 11657705732456630725882. Named by Lori "in honour of our elegant grandmother".

The Keith Group Set [C[1], C[2], C[3], C[4]]=[29 0 5 1922] Corresponds to an elliptic curve of conductor 287854345474. Named by the Lavery family.

The Gimmie Wiekewak Group Set [C[1], C[2], C[3], C[4]]=[1933 0 1949 1951] Corresponds to an elliptic curve of conductor 51362462217075650615474. Named by Calvin.

The Jonathan Blain Group Set [C[1], C[2], C[3], C[4]]=[25 41 12 2009] Corresponds to an elliptic curve of conductor 2244400844581. Named by his brother Nick.

The WEHRWEIN Group Set [C[1], C[2], C[3], C[4]]=[1973 0 1979 1987] Corresponds to an elliptic curve of conductor 14710465782248172436438.

The Lucy Jarman Group Set [C[1], C[2], C[3], C[4]]=[0 0 0 19489] Corresponds to an elliptic curve of conductor 24308551744.

The James Howe Group Set [C[1], C[2], C[3], C[4]]=[30 0 1 2010] Corresponds to an elliptic curve of conductor 2789915804973. Named by Ameli Gottstein for James's birthday. It's actually the prize for the Greenwich Christmas maths competition, which was won for the second year in a row by Ameli Gottstein, and since she already has a group named after her because she won it last year, she's asked for one for James as her birthday present for him!

The Hutchinson-Harte Group Set [C[1], C[2], C[3], C[4]]=[4 5 14 2131] Corresponds to an elliptic curve of conductor 637765256384.

The Michael Group Set [C[1], C[2], C[3], C[4]]=[9 0 7 1987] Corresponds to an elliptic curve of conductor 62433804878.

The Brothbri Group Set [C[1], C[2], C[3], C[4]]=[1993 0 1997 1999] Corresponds to an elliptic curve of conductor 62824653885895079710166.

The Mabey Group Set [C[1], C[2], C[3], C[4]]=[14 0 2 2010] Corresponds to an elliptic curve of conductor 37325897240. "In honor of my husband for Valentine's Day in our name "Mabey." We met in a calculus class so this is a fitting gift."

The Pillinger-Cork Group Set [C[1], C[2], C[3], C[4]]=[2003 0 2011 2017] Corresponds to an elliptic curve of conductor 130904249021155079862106.

The Martin Group Set [C[1], C[2], C[3], C[4]]=[18,0,3,1957] Corresponds to an elliptic curve of conductor 86570025499. Named by Rosemary Phillips for her husband's birthday. "He is a physicist, not a mathematician!"

The Bruce Eyley Group Set [C[1], C[2], C[3], C[4]]=[5 0 3 1961] Corresponds to an elliptic curve of conductor 485757218386. Named by Siobhan and Zac Eyley for their Dad's birthday. "This is an awesome idea, one that I read about in someone else's paper on a very boring train journey and had to steal half a page so I could donate once I got home."

The Katrin Group Set [C[1], C[2], C[3], C[4]]=[2017 0 2027 2029] Corresponds to an elliptic curve of conductor 137433798921676185125674. Named by Jon Sutton.

The Andrew Rivett Group Set [C[1], C[2], C[3], C[4]]=[16 0 3 2010] Corresponds to an elliptic curve of conductor 89126386905. Named by Charlie Khan for Andrew's birthday.

The Paul Cooper Group Set [C[1], C[2], C[3], C[4]]=[23 0 3 2010] Corresponds to an elliptic curve of conductor 356603622. Named by Rachael Graves for Paul's birthday.

The Grifafterbroydandthewilliwizup Group Set [C[1], C[2], C[3], C[4]]=[60 0 60 24] Corresponds to an elliptic curve of conductor 6062416092. For the team that made the best maths clock.

The Joel Rees Group Set [C[1], C[2], C[3], C[4]]=[2039 0 2053 2063] Corresponds to an elliptic curve of conductor 6791656376802946335170.

The Ada Thireou Group Set [C[1], C[2], C[3], C[4]]=[2 0 4 2010] Corresponds to an elliptic curve of conductor 261380113760. Named by Prodromos E. Atlamazoglou for Ada's birthday.

The Eric Werley Group Set [C[1], C[2], C[3], C[4]]=[2069 0 2081 2083] Corresponds to an elliptic curve of conductor 20563241482931075918578.

These objects live in hyperspace, beyond the 3-dimensional world that we inhabit. So it is impossible to draw pictures or make models of them. Instead, we use the powerful language of mathematics and in particular group theory to explore their properties. The complicated formula at the top of the post describes how the symmetries inside this object can be built by taking combinations of 9 basic symmetries called a

_{1},a

_{2},a

_{3},b

_{1},b

_{2},b

_{3},X,Y,Z. The complicated formula tells you how these symmetries interact with each other. For example if you do symmetry a

_{1}followed by b

_{2}, the formula tells you that that leaves the object in the same position as if you'd first done symmetry X first then b

_{2}and then a

_{1}.

A similar thing happens with objects we can see. Take a beer mat. Place it on the table. First rotate it 90 degrees clockwise then reflect or flip the mat in the vertical line running down the middle of the mat. This is the same as if I start by rotating the beer mat 180 degrees then flip in the vertical then do the rotation by 90 degrees clockwise.

Each symmetrical object constructed above is unique because the symmetries interact with each other in their own special way. Often these interactions are controlled by the numbers in the date of birth of the person after whom the symmetrical object is named. They are special because the structures of these objects are connected to the arithmetic of elliptic curves. Trying to understand solutions to elliptic curves is one of the big open problems in mathematics related to one of the Clay Millennium Problems (The Birch-Swinnerton-Dyer Conjecture). The elliptic curve associated with each group of symmetries is got by taking the numbers [C[1], C[2], C[3], C[4]] and putting them into the following equation:

Y

^{2}+C[1]XY+C[3]Y=X

^{3}+C[2]X

^{2}+C[4]X.

If you would like to explore a little bit more of the mathematical significance of these groups then these two papers are where the first groups I constructed are explained. But, be warned, you'll probably need a maths degree to understand the intricacies of these papers.

A nilpotent group and its elliptic curve: non-uniformity of local zeta functions of groups, Israel J. of Math 126 (2001), 269-288.

Counting subgroups in nilpotent groups and points on elliptic curves, J. Reine Angew. Math. 549 (2002) 1-21.