curve #303

y² + xy + y = x³ − x² − 14418406441122314356613x + 574135768533729332199631492462717

a-invariants: [1, -1, 1, -14418406441122314356613, 574135768533729332199631492462717]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 465635685763725597459079854496238023467975734617660671674730
naive height: 164.6820
Faltings height: 11.7137
discriminant (Δ): 49435758489582663623226776897710037271715557545122875841777670553600
primes of bad reduction: 2, 3, 5, 5889019217, 12754129273, 68882668174529078293938516321916984417
regulator: 843718278546028622.9239499523459486473574173665126346451507378629907049
submitted by: Christopher R. Hill
submitted at: 2026-08-23 20:08:10 UTC
last updated: 2026-08-23 20:20:30 UTC

(-683617917186977/6241, -14283046944005241755008/493039)
(-98149833831515/2209, -3485505877609528933172/103823)
(97173516212095, -957903075109673924992)
(1218632583943/121, -27598432064301364352/1331)
(11097950174017/64, 29359098442111050661/512)
(38859823855, 8515889589736016)
(36594401208086327/170569, -6041837420960395993447424/70444997)
(216705743698162063/1234321, -80598415195711739854692832/1371330631)
(24247123770033991/765625, 8184909782410988891230336/669921875)
(616670120352535/6889, -495804028983498775424/571787)
(83576302044384343/1792921, -4372618772574377310652048/2400721219)
(305940074164099/1225, 4803294575566282458748/42875)
(-225152040788657/5041, 12026146937381689368448/357911)
(-100997307175, 31624999497196756)
(434707683613/16, 910632088997334017/64)
(-40622193867653/324, 118235798585625091321/5832)

Found with Rank Hunter v0.7.13; family=Mestre/Fermigier sextuple, generic rank >=11; parameter=2769/2; local status: rigorous rank lower bound >= 16.

last edited by Christopher R. Hill at 2026-08-23 20:08:10 UTC · history