curve #670

y² + y = x³ − x² − 82x + 622

a-invariants: [0, -1, 1, -82, 622]
rank (lower bound): ≥ 5
torsion subgroup: trivial
conductor (N): 117138251
discriminant (Δ): -117138251
Faltings height: 0.2380
naive height: 26.2997
primes of bad reduction: 117138251
regulator: 36.5120549910847903683077666343795283179820070194
submitted by: David Renshaw
submitted at: 2026-09-08 19:18:25 UTC
last updated: 2026-09-08 19:18:25 UTC

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

(4, 18)
(7, 18)
(-4, 29)
(11, 30)
(2, 21)

Commentary

LMFDB 117138251.a1. Curve data, generators (4, 18), (7, 18), (-4, 29), (11, 30), (2, 21) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/117138251/a/1

last edited by David Renshaw at 2026-09-08 19:18:25 UTC · history