curve #908

y² + y = x³ − 30x + 63

a-invariants: [0, 0, 1, -30, 63]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/3ℤ
conductor (N): 27
discriminant (Δ): -243
Faltings height: -0.4972
naive height: 21.8173
primes of bad reduction: 3
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 14:59:18 UTC
last updated: 2026-09-23 14:59:18 UTC

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Commentary

Cremona 27a4 = LMFDB 27.a2: https://www.lmfdb.org/EllipticCurve/Q/27/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 27, minimal discriminant -243, torsion ℤ/3ℤ.

last edited by David Renshaw at 2026-09-23 14:59:18 UTC · history