curve #2327

y² + xy = x³ − 582451039220x + 84157259788064400

a-invariants: [1, 0, 0, -582451039220, 84157259788064400]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 131407770
discriminant (Δ): 9586528130674216851747869100096000000
Faltings height: 5.7920
naive height: 92.8851
primes of bad reduction: 2, 3, 5, 13, 47, 67, 107
regulator: 3.743836945105375143602480899898491979643
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:54:38 UTC
last updated: 2026-09-26 19:54:38 UTC

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

(106552, 152608636)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=20; A=(3q-p)(p+q)^3=-2106081, B=-(p+3q)(p-q)^3=3909919. 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 19:54:38 UTC · history