curve #976

y² + xy = x³ − x² + 6x

a-invariants: [1, -1, 0, 6, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/6ℤ
conductor (N): 90
discriminant (Δ): -13500
Faltings height: -0.5184
naive height: 16.8936
primes of bad reduction: 2, 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:08:59 UTC
last updated: 2026-09-23 15:08:59 UTC

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Commentary

Cremona 90a1 = LMFDB 90.a4: https://www.lmfdb.org/EllipticCurve/Q/90/a/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 90, minimal discriminant -13500, torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:09:00 UTC · history