curve #5677

y² + y = x³ + 1093366509354880

a-invariants: [0, 0, 1, 0, 1093366509354880]
c-invariants: [0, -944668664082616536]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 2832432250889733342553290483
discriminant (Δ): -516434539872474190614398900474907
Faltings height: 4.9559
naive height: 82.7792
primes of bad reduction: 3, 7, 61, 23986672649
regulator: 1483099748.426229115696037608366935863527821706418703851217
submitted by: jesper-petersen
submitted at: 2026-10-24 07:32:46 UTC
last updated: 2026-10-24 07:32:46 UTC

Witness: 10 independent points log in to add more points →

(-101260, 7422144)
(-26962, 32768376)
(-1342, 33066056)
(73220, 38547519)
(527345/4, 465431277/8)
(253820, 132081855)
(415898, 270243816)
(2985353/16, 5575382277/64)
(6809369/100, 37537979847/1000)
(2238334/9, 3465750824/27)

Commentary

Exact-rank-10 Mordell curve found using the Burkhardt quartic construction with parameters (u,v,w)=(3,2,1) and specialization t=-221/770 (October 2026). Exact rank [10,10] independently verified using PARI/GP 2.17.4 with ten rational points checked exactly on the curve.

last edited by jesper-petersen at 2026-10-24 07:32:46 UTC · history