curve #1066

y² + xy = x³ − 35358150x + 80924422500

a-invariants: [1, 0, 0, -35358150, 80924422500]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 15810
discriminant (Δ): -169462737117000000000
Faltings height: 2.9723
naive height: 63.7568
primes of bad reduction: 2, 3, 5, 17, 31
regulator: 1.001590490174866948632670620868054302470
submitted by: David Renshaw
submitted at: 2026-09-23 15:23:59 UTC
last updated: 2026-09-23 15:23:59 UTC

Witness: 1 independent point log in to add more points →

(3420, 330)

Commentary

Cremona 15810u1 = LMFDB 15810.u1: https://www.lmfdb.org/EllipticCurve/Q/15810/u/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 15810, minimal discriminant -169462737117000000000, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.

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