curve #5762

y² = x³ − 6346996267199242478435832675

a-invariants: [0, 0, 0, 0, -6346996267199242478435832675]
c-invariants: [0, 5483804774860145501368559431200]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 2056426790572554563013209786700
discriminant (Δ): -17402844218043362899432239449166168733756616965698187230000
Faltings height: 9.8542
naive height: 141.5587
primes of bad reduction: 2, 3, 5, 7, 13, 43, 73, 109, 359, 823
regulator: 34464980267304.9229746651022732179444786865395884855654
submitted by: Maksym Voznyy
submitted at: 2026-10-24 20:03:29 UTC
last updated: 2026-10-24 20:03:29 UTC

(7018772288313906220096230522123126763731286594093921/3764293848276009191541343462952924740583424, -84970984117908562020350158264571604059939485754635822480213356615390913752431/7303403191539366915634735141820053041466495998648030234025132032)
(15321708934557653335557069841889251/4599333531451121212653849, -1726071097274722810982979393326326564050314808476776/9863756825160971599780573076714133507)
(235114352709259/1089, -3605110457201226362852/35937)
(526082105625246315902510224459/207805749920842636161, 297730662649115895006692843280899347191661148/2995617370734543716037448212159)
(1117899972741130369670627239844633423685105859/473415125050760652560804001595642809, 26899937184977831927917780687919784720343751557596264918835155740552/325734075809641259956019040297474742676955718893372627)
(6813381379479651694605599601469689850019969077671930721/3171756930493264730263935196860690136608844176, 10666391724848915543446795789188613083603880693679039722451655810731452881421502831/178628127733114460320006676821085498214397841202020366568847634976576)
(3302005200985121230686001955169586570969/264242729171833158637959128064, -189434538050791781123154524662938587803450176342240413524253/135832773784541099258949196042710470777536512)
(7032664269157385765218159/3337513744745961, 10576606629586723600379009979775148002/192812237463229012296459)

Voznyy (2023), A = -827934536577330, [r, s, t] = [1, 109, 359] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 20:03:29 UTC · history