curve #2448

y² + xy + y = x³ − 13225139379x + 584031030625306

a-invariants: [1, 0, 1, -13225139379, 584031030625306]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 8928570
discriminant (Δ): 688163662785266463984154740900
Faltings height: 4.5994
naive height: 81.5298
primes of bad reduction: 2, 3, 5, 7, 17, 41, 61
regulator: 5.748302289033972126374287388583740542635
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:13 UTC
last updated: 2026-09-26 20:02:13 UTC

Witness: 1 independent point log in to add more points →

(-257653/4, 273741999/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-10, q=17; A=(3q-p)(p+q)^3=20923, B=-(p+3q)(p-q)^3=807003. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 20:02:13 UTC · history