curve #156

y² + xy = x³ − x² − 759880x + 142095100

a-invariants: [1, -1, 0, -759880, 142095100]
c-invariants: [36474249, -122606032293]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 1938196651043119330
discriminant (Δ): 19381966510431193300
Faltings height: 2.3991
naive height: 52.2364
primes of bad reduction: 2, 5, 637771, 303901659223
regulator: 100835.16934808000041574528314722060871634978015464820244
submitted by: Edgar Costa
submitted at: 2026-06-24 21:09:14 UTC
last updated: 2026-07-01 22:52:28 UTC

Witness: 9 independent points log in to add more points →

(11, 11559)
(-37, -13026)
(38, 10624)
(-50, -13390)
(-103, -14756)
(110, 7680)
(130, 6680)
(135, 6410)
(147, 5719)

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 21:09:14 UTC · history