curve #1077

y² + xy + y = x³ − x² − 475589417x + 3992151134441

a-invariants: [1, -1, 1, -475589417, 3992151134441]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/12ℤ
conductor (N): 117810
discriminant (Δ): 74390985884565504000000
Faltings height: 3.5746
naive height: 71.5538
primes of bad reduction: 2, 3, 5, 7, 11, 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:25:06 UTC
last updated: 2026-09-23 15:25:06 UTC

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Commentary

Cremona 117810el3 = LMFDB 117810.ei4: https://www.lmfdb.org/EllipticCurve/Q/117810/ei/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 117810, minimal discriminant 74390985884565504000000, torsion ℤ/12ℤ.

last edited by David Renshaw at 2026-09-23 15:25:06 UTC · history