curve #5610

y² = x³ − 256624626608047

a-invariants: [0, 0, 0, 0, -256624626608047]
c-invariants: [0, 221723677389352608]
rank (lower bound): ≥ 11
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 2370823163341903594820345551524
discriminant (Δ): -28449877960102843137844146618288
Faltings height: 4.7144
naive height: 79.8804
primes of bad reduction: 2, 3, 1753, 146391686599
regulator: 542058292465.631529336872237080951865950117014598388150430292
submitted by: jesper-petersen
submitted at: 2026-10-23 22:41:18 UTC
last updated: 2026-10-23 22:41:18 UTC

Witness: 11 independent points log in to add more points →

(166207, 65839236)
(1113131, 1174299862)
(910732238, 27484387622915)
(1876286/25, 1611089591/125)
(3202297/16, 5638038669/64)
(18367564/289, 1524077799/4913)
(33276092/121, 190766700139/1331)
(511432969/7744, 3820309541019/681472)
(603682184/6889, 11666201724131/571787)
(710727344/2809, 18796919126539/148877)
(1450478659/9, 55241697459554/27)

Commentary

Exact-rank-11 Mordell curve discovered in October 2026 using the Burkhardt quartic construction, with parameters (u,v,w)=(11,-8,2) and specialization t=-645/722.

last edited by jesper-petersen at 2026-10-23 22:41:18 UTC · history