curve #1017

y² + xy = x³ − 75x + 225

a-invariants: [1, 0, 0, -75, 225]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 330
discriminant (Δ): 3920400
Faltings height: 0.0069
naive height: 24.5669
primes of bad reduction: 2, 3, 5, 11
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:16:28 UTC
last updated: 2026-09-23 15:16:28 UTC

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Commentary

Cremona 330b2 = LMFDB 330.e4: https://www.lmfdb.org/EllipticCurve/Q/330/e/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 330, minimal discriminant 3920400, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:16:28 UTC · history