curve #2172

y² = x³ − x² − 10428240x + 9127296000

a-invariants: [0, -1, 0, -10428240, 9127296000]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 14769840
discriminant (Δ): 36617902166962852761600
Faltings height: 3.0356
naive height: 60.0937
primes of bad reduction: 2, 3, 5, 19, 41, 79
regulator: 58.343701545475895555207749666826711159366458
submitted by: Steps Unbounded
submitted at: 2026-09-26 14:55:43 UTC
last updated: 2026-09-26 14:55:43 UTC

Witness: 3 independent points log in to add more points →

(-2320, 144320)
(-2415, 142200)
(-2688, 133152)

Commentary

Height-ordered search of the universal family for torsion Z/2Z x Z/4Z (Tate/Kubert normal form, parameter t=15/19), smallest curves first; rank lower bound from PARI ellrank: 3 independent points.

last edited by Steps Unbounded at 2026-09-26 14:55:43 UTC · history