curve #644

y² + xy + y = x³ − 174327769786445569143685x + 26865014546188354102268547317071580

a-invariants: [1, 0, 1, -174327769786445569143685, 26865014546188354102268547317071580]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 3526659576444332003065968948933523393292258533402033878
discriminant (Δ): 27275519685621367537479936157925352420919607455816618866249844471758084
Faltings height: 12.2765
naive height: 172.1593
primes of bad reduction: 2, 3, 7, 19, 37, 61, 431, 281251, 1849681, 4108529, 2125565790093337203135315017
regulator: 4606759944219447.7361488598438638378794718067085933420693708325684633379707
submitted by: David Renshaw
submitted at: 2026-09-08 18:50:38 UTC
last updated: 2026-09-08 18:50:38 UTC

(280895695159, 7773957130606508)
(425956962685, 172899280554796280)
(350678772229, 94110924682363808)
(287120248375, 21945508701362444)
(199176821167, 6677330701070864)
(285628949167, 19356497052194864)
(-268396811492, 233065729441007507)
(142880276065, 69813130152131354)
(-103624458782, 209324949886139474)
(-469049498951, 73749754211736458)
(192068835268, 21623645732195432)
(935835403855, 826628978510374664)
(755912315713, 571855719021860954)
(198653413765, 8584954593762080)
(163465145257, 52310802120190508)
(-459604603967, 99507223810175834)
(286462158124, 20831390774299667)
(290165560015, -26681491433462920)

Mestre/Fermigier construction with roots [0,337,475,896,1287,1541] at t=1159/3.

last edited by David Renshaw at 2026-09-08 18:53:23 UTC · history