curve #152

y² + xy = x³ − x² − 1495909x + 697025989

a-invariants: [1, -1, 0, -1495909, 697025989]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 572200654902875954
naive height: 54.2683
Faltings height: 2.3907
discriminant (Δ): 4577605239223007632
primes of bad reduction: 2, 286100327451437977
regulator: 102844.25924766478156295600134311296324227256181616231024
submitted by: Edgar Costa
submitted at: 2026-06-24 21:09:05 UTC
last updated: 2026-07-01 22:53:26 UTC

Witness: 9 independent points

(19, 25848)
(-106, -29177)
(-122, -29565)
(161, 21375)
(187, 20493)
(273, 17440)
(-317, -33595)
(-354, -34205)
(405, 12347)

Commentary

Found by the ec-smallcond GPU integral-point search (Elkies-Watkins style large-rank/small-conductor sweep); rank >= 9 certified from 9 independent points via PARI/GP ellrank (returned rank exactly 9).

last edited by Edgar Costa at 2026-06-24 21:09:05 UTC · history