Torsion group Z/8Z, rank = 6

Elkies (2006)

y2 + xy + y = x3 + x2 + 690560257169377937125059126423812540x  
             - 33492188518937203020097127431557287129957999127407035

	Torsion points:

O, [48336483394805853, -24168241697402927], [883542747769245853, 1125336842235356652764997073], 
[883542747769245853, -1125336843118899400534242927], [4005178026762805853, 8184203792297326700054597073], 
[224631009320286053, 364641927591846714613884873], [4005178026762805853, -8184203796302504726817402927], 
[224631009320286053, -364641927816477723934170927]

	Independent points of infinite order:

P1 = [286126088836986533, 433035480275757031966872273]
P2 = [121390141610245853, 228306310388654208874997073]
P3 = [377567526557995573, 530156507956449179371813753]
P4 = [210538669890805853, 348180841544471134046597073]
P5 = [20853081120020405853, 95301363213306571952478597073]
P6 = [326728698269569003, 476458277653995656563456173]
Some curves with torsion group Z/8Z and rank = 5
High rank curves with prescribed torsion Andrej Dujella home page