curve #3352

y² = x³ − 60501x + 1845740

a-invariants: [0, 0, 0, -60501, 1845740]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 50089248
discriminant (Δ): 12701472123852864
Faltings height: 1.7820
naive height: 44.6448
primes of bad reduction: 2, 3, 11, 97, 163
regulator: 63.28248322148087395477429128767029427244138278
submitted by: David Renshaw
submitted at: 2026-09-26 21:10:35 UTC
last updated: 2026-09-26 21:10:35 UTC

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

(-163, 2716)
(-97, 2608)
(904, 26190)
(-167/4, 16587/8)

Commentary

Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = 198, b = 489; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 50089248, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:10:35 UTC · history