curve #3379

y² = x³ − 274701x + 54429460

a-invariants: [0, 0, 0, -274701, 54429460]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 96183648
discriminant (Δ): 46834676596851264
Faltings height: 1.9895
naive height: 49.1839
primes of bad reduction: 2, 3, 11, 97, 313
regulator: 73.52973821793387033625966018988352496955511902
submitted by: David Renshaw
submitted at: 2026-09-26 21:17:34 UTC
last updated: 2026-09-26 21:17:34 UTC

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

(-313, 10476)
(560, 8730)
(-1543/4, 81189/8)
(9/4, 58685/8)

Commentary

Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = 66, b = 939; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 96183648, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:17:34 UTC · history