curve #1025

y² + xy = x³ + 714x − 82908

a-invariants: [1, 0, 0, 714, -82908]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 546
discriminant (Δ): -2997011332224
Faltings height: 1.0736
naive height: 36.1756
primes of bad reduction: 2, 3, 7, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:17:33 UTC
last updated: 2026-09-23 15:17:33 UTC

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Commentary

Cremona 546f1 = LMFDB 546.f2: https://www.lmfdb.org/EllipticCurve/Q/546/f/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 546, minimal discriminant -2997011332224, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:17:33 UTC · history