curve #945

y² + xy = x³ − x² − 3x + 3

a-invariants: [1, -1, 0, -3, 3]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/3ℤ
conductor (N): 54
discriminant (Δ): -54
Faltings height: -0.8645
naive height: 15.1170
primes of bad reduction: 2, 3
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:04:40 UTC
last updated: 2026-09-23 15:04:40 UTC

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Commentary

Cremona 54a3 = LMFDB 54.a2: https://www.lmfdb.org/EllipticCurve/Q/54/a/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 54, minimal discriminant -54, torsion ℤ/3ℤ.

last edited by David Renshaw at 2026-09-23 15:04:40 UTC · history