curve #3362

y² = x³ − x² − 108241x + 108241

a-invariants: [0, -1, 0, -108241, 108241]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 142443840
discriminant (Δ): 81160990215782400
Faltings height: 1.9341
naive height: 46.3900
primes of bad reduction: 2, 3, 5, 7, 11, 41, 47
regulator: 24.74877520278936502061547961309322887660444835
submitted by: David Renshaw
submitted at: 2026-09-26 21:12:14 UTC
last updated: 2026-09-26 21:12:14 UTC

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

(-245, 3444)
(-175, 3696)
(903, 25256)
(4921, 344400)

Commentary

Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = 328, b = 658; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 142443840, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:12:14 UTC · history