curve #989

y² + xy + y = x³ + x² + 10x − 45

a-invariants: [1, 1, 1, 10, -45]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/5ℤ
conductor (N): 110
discriminant (Δ): -1100000
Faltings height: -0.1596
naive height: 21.3060
primes of bad reduction: 2, 5, 11
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:11:09 UTC
last updated: 2026-09-23 15:11:09 UTC

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Commentary

Cremona 110a1 = LMFDB 110.b2: https://www.lmfdb.org/EllipticCurve/Q/110/b/2 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 110, minimal discriminant -1100000, torsion ℤ/5ℤ.

last edited by David Renshaw at 2026-09-23 15:11:09 UTC · history