curve #1069

y² + xy + y = x³ − x² − 3606647x + 2637610319

a-invariants: [1, -1, 1, -3606647, 2637610319]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/9ℤ
conductor (N): 35910
discriminant (Δ): -810819072000000000
Faltings height: 2.4475
naive height: 56.9087
primes of bad reduction: 2, 3, 5, 7, 19
regulator: 1.798177555696920737888940841223136132479
submitted by: David Renshaw
submitted at: 2026-09-23 15:24:00 UTC
last updated: 2026-09-23 15:24:00 UTC

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

(1077, 736)

Commentary

Cremona 35910bt3 = LMFDB 35910.by1: https://www.lmfdb.org/EllipticCurve/Q/35910/by/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 35910, minimal discriminant -810819072000000000, torsion ℤ/9ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:24:00 UTC · history