curve #975

y² + xy = x³ + x² − x

a-invariants: [1, 1, 0, -1, 0]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ
conductor (N): 89
discriminant (Δ): 89
Faltings height: -0.9135
naive height: 12.8714
primes of bad reduction: 89
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 89b2 = LMFDB 89.b1: https://www.lmfdb.org/EllipticCurve/Q/89/b/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 89, minimal discriminant 89, torsion ℤ/2ℤ.

last edited by David Renshaw at 2026-09-23 15:08:59 UTC · history