curve #1013

y² + xy + y = x³ + x² − 39x + 36

a-invariants: [1, 1, 1, -39, 36]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 231
discriminant (Δ): 2614689
Faltings height: -0.0704
naive height: 22.6059
primes of bad reduction: 3, 7, 11
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:15:25 UTC
last updated: 2026-09-23 15:15:25 UTC

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Commentary

Cremona 231a2 = LMFDB 231.a3: https://www.lmfdb.org/EllipticCurve/Q/231/a/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 231, minimal discriminant 2614689, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:15:25 UTC · history