curve #155

y² + xy = x³ − x² − 1188709x + 494972209

a-invariants: [1, -1, 0, -1188709, 494972209]
c-invariants: [57058041, -427399227405]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 893866404426681866
discriminant (Δ): 1787732808853363732
Faltings height: 2.3223
naive height: 53.5787
primes of bad reduction: 2, 347, 34147, 37719036437
regulator: 416895.39959299299883511375405071915406693053311770994384
submitted by: Edgar Costa
submitted at: 2026-06-24 21:09:12 UTC
last updated: 2026-07-01 22:52:29 UTC

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

(48, 20905)
(65, 20412)
(212, 15783)
(-228, -27347)
(260, 14133)
(-260, -27913)
(-293, -28455)
(329, 11643)
(404, 8773)

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 21:09:12 UTC · history