curve #1063

y² + xy + y = x³ − x² − 20391107x + 35440483331

a-invariants: [1, -1, 1, -20391107, 35440483331]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/12ℤ
conductor (N): 8190
discriminant (Δ): 180256538109375000000
Faltings height: 2.8872
naive height: 62.1054
primes of bad reduction: 2, 3, 5, 7, 13
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:22:56 UTC
last updated: 2026-09-23 15:22:56 UTC

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Commentary

Cremona 8190bv8 = LMFDB 8190.bx1: https://www.lmfdb.org/EllipticCurve/Q/8190/bx/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 8190, minimal discriminant 180256538109375000000, torsion ℤ/12ℤ.

last edited by David Renshaw at 2026-09-23 15:22:56 UTC · history