curve #994

y² + y = x³ − x² + x

a-invariants: [0, -1, 1, 1, 0]
rank (lower bound): ≥ 1
torsion subgroup: trivial
conductor (N): 131
discriminant (Δ): -131
Faltings height: -0.9110
naive height: 12.1735
primes of bad reduction: 131
regulator: 0.2160951986677483660829254961619972058465
submitted by: David Renshaw
submitted at: 2026-09-23 15:12:12 UTC
last updated: 2026-09-23 15:12:12 UTC

Witness: 1 independent point log in to add more points →

(0, 0)

Commentary

Cremona 131a1 = LMFDB 131.a1: https://www.lmfdb.org/EllipticCurve/Q/131/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 131, minimal discriminant -131, trivial torsion. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:12:12 UTC · history