Torsion group Z/2Z × Z/2Z, rank = 15


Elkies (2009)

y2 + xy = x3 - x2 - 1478818379630960182018543975144238479079598870400357903794x
    + 21612333371564362906227820064846376685227380006732368388851217276076518563786908263808	 

	Torsion points: 

O, [20132796920323657380201007272, -10066398460161828690100503636],
[-44342063964345914112746632512, 22171031982172957056373316256],
[96837068176089026930182500963/4, -96837068176089026930182500963/8]


	Independent points of infinite order:

P1 = [11183035360176737872066462162, 2544250119932764965168254926681650601072814]
P2 = [-14387255078284602255172684728, 6317468477138182570583042837408855896541364]
P3 = [19438262913631476179745098142, 459721721339879324467548812793427818227814]
P4 = [55823249110172914794349281022, 10631004522185171552847940461954446457166364]
P5 = [32572289692579628851611993897, 2828698563670717423033345745417611680180114]
P6 = [24588470142629085616740326022, 341270246931310610931397778424345615952614]
P7 = [19982025847826040867579006207, 202476372279358043207285606116969759878864]
P8 = [24988563558081184745544566922, 512203846743830750521268371377174156493614]
P9 = [19409175712041011823546618522, 470570514278064910180708844073966212677614]
P10 = [15343558255011251183303194179, 1591933177167506122828050814070561825165145]
P11 = [24354530036362110771030330897, 205253458293167433649155238598749814431989]
P12 = [40442125414745602621502494162, 5286919745747422460169589189761390362993024]
P13 = [24943293985561753095203275747, 494620041717645188762260334392615608575364]
P14 = [266053292109858198648954299847, 135869710793553829756471002267336612487527489]
P15 = [1872527673822446130016910594397, 2561836921226411679741258783032933091672508614]

Some curves with torsion group Z/2Z × Z/2Z and rank = 10, 11, 12 or 14
High rank curves with prescribed torsion Andrej Dujella home page