curve #953

y² + y = x³ + x² + 20x − 32

a-invariants: [0, 1, 1, 20, -32]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/5ℤ
conductor (N): 57
discriminant (Δ): -1121931
Faltings height: -0.1533
naive height: 20.8163
primes of bad reduction: 3, 19
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:05:44 UTC
last updated: 2026-09-23 15:05:44 UTC

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Commentary

Cremona 57c1 = LMFDB 57.b2: https://www.lmfdb.org/EllipticCurve/Q/57/b/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 57, minimal discriminant -1121931, torsion ℤ/5ℤ.

last edited by David Renshaw at 2026-09-23 15:05:44 UTC · history