curve #590

y² + xy = x³ − x² − 37987453366x + 3315640089106648

a-invariants: [1, -1, 0, -37987453366, 3315640089106648]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 620410434799344097520433283935898
discriminant (Δ): -1240820869598688195040866567871796
Faltings height: 5.0723
naive height: 84.9980
primes of bad reduction: 2, 200987, 1445653687, 1067620396002827521
regulator: 197773219110.140314586034428224567071471381132215495126261412374274
submitted by: Michael Rubinstein
submitted at: 2026-09-05 22:17:45 UTC
last updated: 2026-09-05 22:17:45 UTC

(-227154, 15070108)
(-200594, 53618268)
(-188532, 61545248)
(-177361, 66975732)
(-49002, 71154214)
(-36843, 68320690)
(-756, 57830804)
(11551, 53644836)
(41146, 42667446)
(93548, 24049764)
(127574, 23296422)
(144714, 29064032)
(150269, 31555177)
(1663949/16, 1413110073/64)

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

last edited by Michael Rubinstein at 2026-09-05 22:17:45 UTC · history