curve #993

y² + y = x³ − x² + x − 1

a-invariants: [0, -1, 1, 1, -1]
rank (lower bound): ≥ 1
torsion subgroup: trivial
conductor (N): 123
discriminant (Δ): -123
Faltings height: -0.9162
naive height: 12.0995
primes of bad reduction: 3, 41
regulator: 0.2919145287294710320057605948504386772462
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 →

(1, 0)

Commentary

Cremona 123b1 = LMFDB 123.b1: https://www.lmfdb.org/EllipticCurve/Q/123/b/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 123, minimal discriminant -123, 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