curve #5604

y² + y = x³ + 3466989542317276424

a-invariants: [0, 0, 1, 0, 3466989542317276424]
c-invariants: [0, -2995478964562126830552]
rank (lower bound): ≥ 12
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 2374324244254292909372143153853800689
discriminant (Δ): -5192647122184138592796877077478262106843
Faltings height: 6.2996
naive height: 98.9028
primes of bad reduction: 3, 239, 1619, 84947, 15626293
regulator: 30625914150572.898993408543610718116339548971899998178024554868
submitted by: jesper-petersen
submitted at: 2026-10-23 22:23:58 UTC
last updated: 2026-10-23 22:23:58 UTC

(-664224, 1781554999)
(1434268, 2533270152)
(4931452, 11108377463)
(-547308431/484, 15137457058085/10648)
(6595446/25, 233363692256/125)
(753094756/441, 26915965970795/9261)
(20730942993/8464, 3318404017545113/778688)
(6264509322/5929, 984095065625531/456533)
(91866158094/169, 27844109697181675/2197)
(96101664034/81225, 52397013587882923/23149125)
(744241614582/885481, 1679080326337466411/833237621)
(174007428769462/34257609, 2325529234320537803104/200509785477)

Rank-12 Mordell curve constructed using the Burkhardt quartic family, with parameters (u,v,w)=(-2,-9,-12) and specialization t=407/102.

last edited by jesper-petersen at 2026-10-23 22:23:58 UTC · history