curve #2667

y² + xy + y = x³ − x² − 3x

a-invariants: [1, -1, 1, -3, 0]
rank (lower bound): ≥ 2
torsion subgroup: trivial
conductor (N): 1171
discriminant (Δ): 1171
Faltings height: -0.7204
naive height: 14.5794
primes of bad reduction: 1171
regulator: 0.336702983678594590092633836904224732983202
submitted by: David Renshaw
submitted at: 2026-09-26 20:16:46 UTC
last updated: 2026-09-26 20:16:46 UTC

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

(0, 0)
(-1, 1)

Commentary

Cremona 1171a1 = LMFDB 1171.a1: https://www.lmfdb.org/EllipticCurve/Q/1171/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 1171, minimal discriminant 1171, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:16:46 UTC · history