curve #671

y² + y = x³ − x² − 400x + 3262

a-invariants: [0, -1, 1, -400, 3262]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 122882843
discriminant (Δ): -122882843
Faltings height: 0.3501
naive height: 29.6200
primes of bad reduction: 122882843
regulator: 32.6808647548453731300948854599525267400060318117
submitted by: David Renshaw
submitted at: 2026-09-08 19:18:32 UTC
last updated: 2026-09-08 19:18:32 UTC

Witness: 5 independent points log in to add more points →

(11, 8)
(13, 9)
(14, 14)
(7, 27)
(20, 53)

Commentary

LMFDB 122882843.a1. Curve data, generators (11, 8), (13, 9), (14, 14), (7, 27), (20, 53) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/122882843/a/1

last edited by David Renshaw at 2026-09-08 19:18:32 UTC · history