curve #1016

y² + xy + y = x³ − x² + x

a-invariants: [1, -1, 1, 1, 0]
rank (lower bound): ≥ 1
torsion subgroup: trivial
conductor (N): 297
discriminant (Δ): -297
Faltings height: -0.8393
naive height: 12.4806
primes of bad reduction: 3, 11
regulator: 0.3146944998668636367163098982530917719998
submitted by: David Renshaw
submitted at: 2026-09-23 15:16:28 UTC
last updated: 2026-09-23 15:16:28 UTC

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

(0, 0)

Commentary

Cremona 297b1 = LMFDB 297.b1: https://www.lmfdb.org/EllipticCurve/Q/297/b/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 297, minimal discriminant -297, trivial torsion. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:16:28 UTC · history