curve #3360

y² = x³ − x² − 68630x − 4402200

a-invariants: [0, -1, 0, -68630, -4402200]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 442345440
discriminant (Δ): 12229343018049600
Faltings height: 1.7889
naive height: 45.0231
primes of bad reduction: 2, 3, 5, 17, 151, 359
regulator: 125.1956230128947142272164891656582027142243164
submitted by: David Renshaw
submitted at: 2026-09-26 21:11:55 UTC
last updated: 2026-09-26 21:11:55 UTC

Witness: 4 independent points log in to add more points →

(-190, 1320)
(-169, 1530)
(-118, 1428)
(-73, 462)

Commentary

Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = -151, b = -510; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 442345440, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:11:55 UTC · history