curve #951

y² + xy + y = x³ − 7x + 5

a-invariants: [1, 0, 1, -7, 5]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 57
discriminant (Δ): 3249
Faltings height: -0.5916
naive height: 17.2386
primes of bad reduction: 3, 19
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:05:43 UTC
last updated: 2026-09-23 15:05:43 UTC

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Commentary

Cremona 57b1 = LMFDB 57.c2: https://www.lmfdb.org/EllipticCurve/Q/57/c/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 57, minimal discriminant 3249, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:05:43 UTC · history