curve #1033

y² + xy + y = x³ + x² − 70244x + 7127525

a-invariants: [1, 1, 1, -70244, 7127525]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/8ℤ
conductor (N): 714
discriminant (Δ): 55468445663232
Faltings height: 1.5394
naive height: 45.0928
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 714g1 = LMFDB 714.f5: https://www.lmfdb.org/EllipticCurve/Q/714/f/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 714, minimal discriminant 55468445663232, torsion ℤ/8ℤ.

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