curve #5614

y² = x³ + 389909352168349433

a-invariants: [0, 0, 0, 0, 389909352168349433]
c-invariants: [0, -336881680273453910112]
rank (lower bound): ≥ 12
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 111694998055108364588230797740636196
discriminant (Δ): -65676658856403718377879709071494083248
Faltings height: 5.9354
naive height: 94.5325
primes of bad reduction: 2, 3, 7, 23, 6555427, 52776277
regulator: 1626294641404.8917428842815198662472910306730761180778413152707
submitted by: jesper-petersen
submitted at: 2026-10-23 23:07:28 UTC
last updated: 2026-10-23 23:07:28 UTC

Witness: 12 independent points log in to add more points →

(-518734, 500325727)
(7616, 624427573)
(721466, 874895377)
(741398, 892991785)
(918682, 1079469999)
(962476, 1132037397)
(1075084196, 35250372980437)
(-176006878/289, 1989735838735/4913)
(4273217/4, 10148141695/8)
(220638019/625, 10292406045978/15625)
(699886441/1936, 56321734082613/85184)
(314626688026/724201, 423367560444547803/616295051)

Commentary

Exact-rank-12 Mordell curve discovered in October 2026 using the Burkhardt quartic construction, with parameters (u,v,w)=(1,3,-3) and specialization t=491/711.

last edited by jesper-petersen at 2026-10-23 23:07:29 UTC · history