curve #980

y² + y = x³ + x

a-invariants: [0, 0, 1, 1, 0]
rank (lower bound): ≥ 1
torsion subgroup: trivial
conductor (N): 91
discriminant (Δ): -91
Faltings height: -0.9363
naive height: 11.6136
primes of bad reduction: 7, 13
regulator: 0.1423921506687686591847910949737051319662
submitted by: David Renshaw
submitted at: 2026-09-23 15:10:03 UTC
last updated: 2026-09-23 15:10:03 UTC

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

(0, 0)

Commentary

Cremona 91a1 = LMFDB 91.a1: https://www.lmfdb.org/EllipticCurve/Q/91/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 91, minimal discriminant -91, trivial torsion. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:10:03 UTC · history