curve #5757

y² = x³ − 4407625524343828124403971206587

a-invariants: [0, 0, 0, 0, -4407625524343828124403971206587]
c-invariants: [0, 3808188453033067499485031122491168]
rank (lower bound): ≥ 8
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 17630502097375312497615884826348
discriminant (Δ): -8392534313549992909964150112011100507938283761853418065105461808
Faltings height: 10.9447
naive height: 154.6449
primes of bad reduction: 2, 3, 11, 13, 17, 29, 31, 71, 113, 7681
regulator: 19290172290357.2847502098301782052026520084908070073380
submitted by: Maksym Voznyy
submitted at: 2026-10-24 19:36:27 UTC
last updated: 2026-10-24 19:36:27 UTC

(17277983805549368192320479060581767/1018558609028131307836249, 707367176101955342464142761551648562795279888840450/1027966675035837676824744454311374557)
(629432490683110874361659435015713/23642083705305594665536, 13824848415804100653132227098476200545397232322895/3635202647110766378735516656822784)
(496947941945732785877611069897/21164954692405944484, 284493245512760374961682156087218647485369125/97370189378798208460435412648)
(8176462720888214380991392085731/458937236247166407025, 10980880836476905206001458647469948540781577996/9831730012236963940204025696375)
(65107173283, 16479624900483640)
(243587434136676377164044264093772033/12833291377376343621223876, 71675999376973096615201546147908417654233715478235615/45973448576677305887015383189134312376)
(48930833191397791063/628454761, 340672086688207792300464591350/15754732403509)
(1363438335195476571647300156017470937/54262261145450848394408464, -1352915049489880505727149300108923274399160182311277155/399711672391646306672766279889677978688)

Voznyy (2023), A = -808072743731682, [r, s, t] = [85, 325, 339] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-24 19:36:27 UTC · history