curve #966

y² + xy + y = x³ − x − 1

a-invariants: [1, 0, 1, -1, -1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 69
discriminant (Δ): -207
Faltings height: -0.8740
naive height: 12.8302
primes of bad reduction: 3, 23
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 69a1 = LMFDB 69.a2: https://www.lmfdb.org/EllipticCurve/Q/69/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 69, minimal discriminant -207, torsion ℤ/2ℤ.

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