curve #950

y² = x³ + x + 2

a-invariants: [0, 0, 0, 1, 2]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 56
discriminant (Δ): -1792
Faltings height: -0.6952
naive height: 14.9094
primes of bad reduction: 2, 7
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 56a1 = LMFDB 56.a4: https://www.lmfdb.org/EllipticCurve/Q/56/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 56, minimal discriminant -1792, torsion ℤ/4ℤ.

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