curve #2253

y² + xy = x³ − 12407200042040x + 16799067703460289600

a-invariants: [1, 0, 0, -12407200042040, 16799067703460289600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 111501390
discriminant (Δ): 322455599435721770976855724130304000000
Faltings height: 6.2888
naive height: 102.0615
primes of bad reduction: 2, 3, 5, 7, 11, 13, 47, 79
regulator: 5.794814421177444704350719687221293482139
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:49:57 UTC
last updated: 2026-09-26 19:49:57 UTC

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

(2243440, 504393160)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=32; A=(3q-p)(p+q)^3=-482625, B=-(p+3q)(p-q)^3=24158911. 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 19:49:58 UTC · history