curve #5679

y² + y = x³ − 22926866599578202

a-invariants: [0, 0, 1, 0, -22926866599578202]
c-invariants: [0, 19808812742035566312]
rank (lower bound): ≥ 10
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 3438053538448260349218292587
discriminant (Δ): -227077003616337159370754837945919723
Faltings height: 5.4631
naive height: 88.8653
primes of bad reduction: 3, 7, 43, 383, 32627809
regulator: 46981176007.80580709179693577479071338781438088807962287107
submitted by: jesper-petersen
submitted at: 2026-10-24 07:38:15 UTC
last updated: 2026-10-24 07:38:15 UTC

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

(299538, 62837770)
(424102, 230983077)
(23452353/16, 113160007615/64)
(57173617/196, 119422513813/2744)
(296894962/81, 5114499257773/729)
(303978438/961, 2782230727099/29791)
(698948488/1369, 16811678386121/50653)
(65625076897/91204, 16285908291911115/27543608)
(160623750924/87025, 64257144615294907/25672375)
(1251949282542/1125721, 1389089556313686482/1194389981)

Commentary

Exact-rank-10 Mordell curve discovered in October 2026 using the Burkhardt quartic construction, with parameters (u,v,w)=(-3,2,-4) and specialization t=685/209. Exact rank [10,10] independently verified with PARI/GP 2.17.4 using ten rational points checked exactly on the minimal model.

last edited by jesper-petersen at 2026-10-24 07:38:15 UTC · history