curve #965

y² + y = x³ + x² − 12x − 21

a-invariants: [0, 1, 1, -12, -21]
rank (lower bound): ≥ 0
torsion subgroup: trivial
conductor (N): 67
discriminant (Δ): -67
Faltings height: -0.6753
naive height: 19.1511
primes of bad reduction: 67
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:07:53 UTC
last updated: 2026-09-23 15:07:53 UTC

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Commentary

Cremona 67a1 = LMFDB 67.a1: https://www.lmfdb.org/EllipticCurve/Q/67/a/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 67, minimal discriminant -67, trivial torsion.

last edited by David Renshaw at 2026-09-23 15:07:53 UTC · history