curve #978

y² + xy + y = x³ − x² − 128x + 587

a-invariants: [1, -1, 1, -128, 587]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/6ℤ
conductor (N): 90
discriminant (Δ): 5400
Faltings height: -0.1718
naive height: 26.1624
primes of bad reduction: 2, 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:10:02 UTC
last updated: 2026-09-23 15:10:02 UTC

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Commentary

Cremona 90b2 = LMFDB 90.b2: https://www.lmfdb.org/EllipticCurve/Q/90/b/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 90, minimal discriminant 5400, torsion ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:10:02 UTC · history