curve #3392

y² = x³ − 457036x − 33415440

a-invariants: [0, 0, 0, -457036, -33415440]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 84722624
discriminant (Δ): 5627491645677174784
Faltings height: 2.2892
naive height: 50.7112
primes of bad reduction: 2, 7, 281, 673
regulator: 138.3325219722489223614431309636076533760549693
submitted by: David Renshaw
submitted at: 2026-09-26 21:19:45 UTC
last updated: 2026-09-26 21:19:45 UTC

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

(-586, 5760)
(-298, 8736)
(-186, 6720)
(822, 12096)

Commentary

Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = -562, b = -1346; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 84722624, torsion ℤ/2ℤ × ℤ/2ℤ.

last edited by David Renshaw at 2026-09-26 21:19:45 UTC · history