Torsion group Z/12Z, rank = 4


Fisher (2008)

y2 + xy = x3 - 4422329901784763147754792226039053294186858800x 
         + 98943710602886706347390586357680210847183616798063680624530387016000

	Torsion points:
O, [65868249464984810984140, 9665935032928102104631538081841700], 
[65868249464984810984140, -9665935032993970354096522892825840], 
[214875756474885826065460, 95235748074472305868288820867550640], 
[214875756474885826065460, -95235748074687181624763706693616100], 
[23857758670284167616130, -2648866153098444069578276494864430], 
[-61826537140886222177330, -11663097222144322118606615793148100], 
[-61826537140886222177330, 11663097222206148655747502015325430], 
[23857758670284167616130, 2648866153074586310907992327248300], 
[196145662156603291475199/4, -196145662156603291475199/8], 
[-3797098871685540790688, -10755509660824465103502016697092664], 
[-3797098871685540790688, 10755509660828262202373702237883352]

	Independent points of infinite order: 

P1 = [34041292371237064006426894957396/630763225, 66204769563702181648309208636101377723512158736/15841618395875]
P2 = [-3925299848487219649803111424581267172504307567199407913441245040118981868/137194342227669518519498512006351993035192663119881,
      22842024253754429037657080561785875269591709783412591343934007046468346667249098446804083045186137431599118192/
      1606957173720562553134392492036223587414467589358506324505368702826998453221]
P3 = [34396396322282805835691520585756626787219271296794743776416028880395727371083219104/484900109842890380829228824741997715427442294522315097791225, 
      -4026147990201728861490911090885573676425328113148109355421737093111146075134797898349014124989856774166271766546125841222888/
      337659072927765759013309287184879322340988288683024746195867377940161451743713659393482125]
P4 = [-1360157677325654026821400382914648821099795934113255313220731687021750378269683124822984403863493256698970/
      95210567235402459537983154136285200689965053149892391652528137442637637800647451769,
      370685526171259919765184269719379305784467970007299015848801757929842196923020385238912398229715366382305152064525129755759650894029117089726075578691605210700/
      29378372210259503406799373066960078670967941610317399339241376984463056059070657785847424233217595325991594921693465686427853]

Some curves with torsion group Z/12Z and rank = 3
High rank curves with prescribed torsion Andrej Dujella home page