Torsion group Z/3Z, rank = 15


Elkies - Klagsbrun (2020)

y2 + xy + y = x3 - 107404730164187455100283304999195859754632145403x 
            + 48976939778870435455584633601954124477725966045276826839333933204370006

	Torsion points:

O, [20068686794995229328280, 216401364590084404674437763597114797], 
[20068686794995229328280, -216401364590104473361232758826443078]

	Independent points of infinite order:

P1 = [-422511571742285267531345, -137592127148862829770221635303960828]
P2 = [-441007351163624462047670, -102824147331859218513919290250298203]
P3 = [156085384573658420738746, 189776933096927384678335033331045984]
P4 = [-460838553366765681840845, -24574287549951174429604416824455828]
P5 = [4176134452254148300203630, 8510736658900069929975759728364918172]
P6 = [-359187750061494853894325, -203013531407261210327764965678707548]
P7 = [-460188579405761971770845, -30783285810055207778934556373103328]
P8 = [646948036481989988599630, 500266360594011622677409610820423797]
P9 = [339470884962917809004155, 227237649388778691045137980486286672]
P10 = [-126915798498020139215720, -246097512030324095711517097854917203]
P11 = [1045627763773449027515596, 1039180222036999853815782266061861389]
P12 = [17730115810583176883376655, 74644027306445943530330235569361589172]
P13 = [256495517365884675394222, 195711357157735899784726812610011893]
P14 = [-142791994651726392782285, -247794290462672857095557195444679328]
P15 = [1113480161648803705205155, 1144516928010965576054744619118736672]

Some curves with torsion group Z/3Z and rank = 8, 9, 10, 11, 12, 13 or 14
High rank curves with prescribed torsion Andrej Dujella home page