curve #977

y² + xy + y = x³ − x² − 8x + 11

a-invariants: [1, -1, 1, -8, 11]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/6ℤ
conductor (N): 90
discriminant (Δ): -8640
Faltings height: -0.5184
naive height: 17.9926
primes of bad reduction: 2, 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:09:00 UTC
last updated: 2026-09-23 15:09:00 UTC

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Commentary

Cremona 90b1 = LMFDB 90.b3: https://www.lmfdb.org/EllipticCurve/Q/90/b/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 90, minimal discriminant -8640, torsion ℤ/6ℤ.

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