curve #934

y² = x³ − 2x + 1

a-invariants: [0, 0, 0, -2, 1]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/4ℤ
conductor (N): 40
discriminant (Δ): 80
Faltings height: -0.8954
naive height: 13.6930
primes of bad reduction: 2, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:02:33 UTC
last updated: 2026-09-23 15:02:33 UTC

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Commentary

Cremona 40a3 = LMFDB 40.a3: https://www.lmfdb.org/EllipticCurve/Q/40/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 40, minimal discriminant 80, torsion ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:02:33 UTC · history