curve #1031

y² + xy = x³ − 1661x + 26097

a-invariants: [1, 0, 0, -1661, 26097]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/7ℤ
conductor (N): 678
discriminant (Δ): -4048994304
Faltings height: 0.6715
naive height: 33.8729
primes of bad reduction: 2, 3, 113
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:18:37 UTC
last updated: 2026-09-23 15:18:37 UTC

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Commentary

Cremona 678d1 = LMFDB 678.e2: https://www.lmfdb.org/EllipticCurve/Q/678/e/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 678, minimal discriminant -4048994304, torsion ℤ/7ℤ.

last edited by David Renshaw at 2026-09-23 15:18:37 UTC · history