curve #737

y² + xy = x³ − 2788197723414759881581426409385x + 1793687065379323276904205672808349144893035225

a-invariants: [1, 0, 0, -2788197723414759881581426409385, 1793687065379323276904205672808349144893035225]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 5745932247948358625427592409401576733924557139961681884130
naive height: 221.9244
Faltings height: 16.2653
discriminant (Δ): -2642292438436287213148380446452007902821930673897011865401810864366417566514934133760000000
primes of bad reduction: 2, 3, 5, 7, 11, 13, 29, 41, 43, 47, 73, 109, 677, 14781515860297024393923302273753248669831
regulator: 1208539094260698.6678052057807066955390484300271894133596467748318402859428
submitted by: Valery Asiryan
submitted at: 2026-09-16 17:40:55 UTC
last updated: 2026-09-16 17:40:55 UTC

Witness: 18 independent points log in to add more points →

(-713381263593198, -58478082757389016040709)
(3329251562949351255/5476, -7285771391108797322851954515/405224)
(836557549313370, -6829792043680539074685)
(940321719625620, -1822442167041629960685)
(945324049880762, -1647355406941330103293)
(963743140504410, -1306168293010428542685)
(965287287566010, -1307746557996676778685)
(973222885786560, -1396327879788502081125)
(977102800693050, -1483409956239836933565)
(985241675888970, -1736003150446671632685)
(296460090212182980/289, -17695600376198324629499655/4913)
(1111169848673370, -8214956032724660738685)
(1226549530846620, -14801172950675508806685)
(2148913785114890, -75666440569264995165805)
(952385864680863670/441, -707994290524670467220336785/9261)
(2349147544733370, -90595565630196461738685)
(74422708723681370, -20297839588627594758402685)
(8526249269068679050/9, -24896389168196431920311130095/27)

Commentary

Specialization T=4/17 of the family identified by wgxli in the commentary to curve #302. The points were obtained by specializing reconstructed generic sections and running minimized quartic searches. The 18 listed points are certified independent by exact quadratic-character certificates.

last edited by Valery Asiryan at 2026-09-16 17:40:55 UTC · history