Torsion group Z/2Z, rank = 19


Elkies (2009)

y2 + xy + y = x3 - x2 + 31368015812338065133318565292206590792820353345x 
         + 302038802698566087335643188429543498624522041683874493555186062568159847

	Torsion points: 

O, [-655364911965298267755181, 327682455982649133877590]

	Independent points of infinite order:

P1 = [-499155234006326082923757, 402509376386904307636088023311932246]
P2 = [14139901902190764472167779, 53177370026792370019660919624681843910]
P3 = [165026138566397083648829, 558309596396209485460849837556760960]
P4 = [463343337635697262499219, 645016881525945325912024782026024790]
P5 = [-428490311544140084738931, 458176166275251046654351925125281840]
P6 = [-3076708833879670305775, 549492732729622717403028037016638716]
P7 = [-37665731401560276357421, 548455893205160937812792765224762710]
P8 = [-589425676522172250643765, 280659706984671022310703064556433246]
P9 = [-481732375371853545253165, 418490225997586738600806619185884118]
P10 = [3690858926941989311074375079, 224228684581316592254479552957274125288710]
P11 = [6130049174458433978294529, 15193625860788829982804926312716459660]
P12 = [99629044314032316202835, 553310835513576760020037678256777046]
P13 = [-336069400109872546513581, 503527960099926164391149483607861590]
P14 = [3296316187302021571885259, 6018489996489383086719697427657451870]
P15 = [239450610550684059490919, 568576446830597022058144468592457990]
P16 = [1116036406771517906484819, 1314196172527374653201729069765173590]
P17 = [1104492511976272577147219, 1297713008801587828896903435227547990]
P18 = [-556915090457934898225581, 334424588793955899397684278466715990]
P19 = [142518206539016399870550419, 1701397854372553501423223969798389683990]

Some curves with torsion group Z/2Z and rank = 14, 15, 16, 17 or 18
High rank curves with prescribed torsion Andrej Dujella home page