curve #1032

y² + xy = x³ − 420x + 3600

a-invariants: [1, 0, 0, -420, 3600]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/8ℤ
conductor (N): 690
discriminant (Δ): -965779200
Faltings height: 0.4599
naive height: 29.9199
primes of bad reduction: 2, 3, 5, 23
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 690k1 = LMFDB 690.k5: https://www.lmfdb.org/EllipticCurve/Q/690/k/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 690, minimal discriminant -965779200, torsion ℤ/8ℤ.

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