curve #1076

y² + xy = x³ − 2276760100x + 41806588162832

a-invariants: [1, 0, 0, -2276760100, 41806588162832]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 110670
discriminant (Δ): 268915325631261926400000000
Faltings height: 4.0683
naive height: 76.2517
primes of bad reduction: 2, 3, 5, 7, 17, 31
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:25:05 UTC
last updated: 2026-09-23 15:25:05 UTC

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Commentary

Cremona 110670cp2 = LMFDB 110670.cm5: https://www.lmfdb.org/EllipticCurve/Q/110670/cm/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 110670, minimal discriminant 268915325631261926400000000, torsion ℤ/2ℤ × ℤ/8ℤ.

last edited by David Renshaw at 2026-09-23 15:25:05 UTC · history