curve #3363

y² = x³ − x² − 200281x + 8534425

a-invariants: [0, -1, 0, -200281, 8534425]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 695117760
discriminant (Δ): 483188700267417600
Faltings height: 2.0841
naive height: 48.2360
primes of bad reduction: 2, 3, 5, 17, 191, 223
regulator: 78.81500916192646038691757528663084285118046572
submitted by: David Renshaw
submitted at: 2026-09-26 21:12:24 UTC
last updated: 2026-09-26 21:12:24 UTC

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

(-339, 6112)
(-297, 6460)
(1953, 84040)
(19525, 2727480)

Commentary

Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = 382, b = 892; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 695117760, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:12:24 UTC · history