curve #4397

y² + xy = x³ − x² − 50804263534x + 2907200305341544

a-invariants: [1, -1, 0, -50804263534, 2907200305341544]
c-invariants: [2438604649641, -2511810090094170645]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 2370568937196628085123918626957166
discriminant (Δ): 4741137874393256170247837253914332
Faltings height: 5.1649
naive height: 85.5673
primes of bad reduction: 2, 1283, 923838245205233080718596503101
regulator: 28844312250790.4608802002194749352963508773391916090015787825549374
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:21:46 UTC
last updated: 2026-10-17 10:21:46 UTC

(-231868, 47245300)
(-2219, 54954945)
(-1260, 54509452)
(-94, 53962774)
(42100, 29012688)
(60627, 7035808)
(477636, 295746184)
(8385559, 24269851253)
(-2202780/49, 24503382856/343)
(-1790636/9, 1938299600/27)
(-3995019/16, 332450885/64)
(685093/16, 1820494703/64)
(678325/49, 16109687159/343)
(51568290/961, 544875973432/29791)

BASE records/rank_14.md#17 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:21:46 UTC · history