curve #2232

y² + xy + y = x³ − 25949401558048x + 50797053184270223006

a-invariants: [1, 0, 1, -25949401558048, 50797053184270223006]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 11199150690
discriminant (Δ): 3602259881584383841665833413966610250000
Faltings height: 6.4808
naive height: 104.2751
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 53, 157
regulator: 4.110080289026052055639367365266510397681
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:40 UTC
last updated: 2026-09-26 19:48:40 UTC

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

(2810680, 255000842)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-52, q=35; A=(3q-p)(p+q)^3=-771341, B=-(p+3q)(p-q)^3=34900659. 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 19:48:40 UTC · history