curve #2246

y² + xy = x³ − 12779262474196x + 16755088633929149840

a-invariants: [1, 0, 0, -12779262474196, 16755088633929149840]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 1172753670
discriminant (Δ): 12289768839066641756537572907186000793600
Faltings height: 6.4491
naive height: 102.1501
primes of bad reduction: 2, 3, 5, 11, 17, 23, 61, 149
regulator: 5.245337113368728162885375891274759805261
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:32 UTC
last updated: 2026-09-26 19:49:32 UTC

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

(-4095952, 619524836)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=44; A=(3q-p)(p+q)^3=2932767, B=-(p+3q)(p-q)^3=26102815. 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 19:49:32 UTC · history