curve #1034

y² + xy = x³ + 108x + 11664

a-invariants: [1, 0, 0, 108, 11664]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/9ℤ
conductor (N): 714
discriminant (Δ): -58763045376
Faltings height: 0.7455
naive height: 32.2501
primes of bad reduction: 2, 3, 7, 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:18:38 UTC
last updated: 2026-09-23 15:18:38 UTC

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Commentary

Cremona 714i1 = LMFDB 714.i3: https://www.lmfdb.org/EllipticCurve/Q/714/i/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 714, minimal discriminant -58763045376, torsion ℤ/9ℤ.

last edited by David Renshaw at 2026-09-23 15:18:38 UTC · history