curve #3072

y² + y = x³ − x² − 24x + 54

a-invariants: [0, -1, 1, -24, 54]
rank (lower bound): ≥ 2
torsion subgroup: trivial
conductor (N): 997
discriminant (Δ): 997
Faltings height: -0.4828
naive height: 21.1891
primes of bad reduction: 997
regulator: 0.249705466521919036772611254371171152496206
submitted by: David Renshaw
submitted at: 2026-09-26 20:35:56 UTC
last updated: 2026-09-26 20:35:56 UTC

Witness: 2 independent points log in to add more points →

(3, 0)
(1, 5)

Commentary

Cremona 997c1 = LMFDB 997.a1: https://www.lmfdb.org/EllipticCurve/Q/997/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 997, minimal discriminant 997, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:35:56 UTC · history