curve #907

y² + y = x³ − 270x − 1708

a-invariants: [0, 0, 1, -270, -1708]
rank (lower bound): ≥ 0
torsion subgroup: trivial
conductor (N): 27
discriminant (Δ): -177147
Faltings height: 0.0521
naive height: 28.4090
primes of bad reduction: 3
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:58:16 UTC
last updated: 2026-09-23 14:58:16 UTC

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Commentary

Cremona 27a2 = LMFDB 27.a1: https://www.lmfdb.org/EllipticCurve/Q/27/a/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 27, minimal discriminant -177147, trivial torsion.

last edited by David Renshaw at 2026-09-23 14:58:16 UTC · history