curve #592

y² + xy = x³ − x² − 51643728544x + 4440535775373364

a-invariants: [1, -1, 0, -51643728544, 4440535775373364]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 148465259769888571900096916876606
discriminant (Δ): 296930519539777143800193833753212
Faltings height: 5.0234
naive height: 85.6165
primes of bad reduction: 2, 2341, 19801, 1601423913452398696160683
regulator: 13877598753.3276450214933979958976167090507927065294486757981821982
submitted by: Michael Rubinstein
submitted at: 2026-09-05 22:59:58 UTC
last updated: 2026-09-05 22:59:58 UTC

(-242917, 51613422)
(-198459, 83003800)
(-55576, 84520558)
(38578, 50037050)
(55681, 41656580)
(56610, 41183338)
(86138, 25079940)
(100385, 16316452)
(146017, 3515963)
(146727, 4600858)
(164273, 19662580)
(175946, 28209810)
(179607, 30875018)
(244075, 79726142)

From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-05 22:59:58 UTC · history