curve #2446

y² + xy = x³ − 2161414664906x + 1223080916764694820

a-invariants: [1, 0, 0, -2161414664906, 1223080916764694820]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 143827530
discriminant (Δ): 536877970185047874978263961600
Faltings height: 5.4768
naive height: 96.8190
primes of bad reduction: 2, 3, 5, 7, 11, 19, 29, 113
regulator: 8.374247218019920536922591977121073304133
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:06 UTC
last updated: 2026-09-26 20:02:06 UTC

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

(2500207/4, 2725561613/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-29, q=28; A=(3q-p)(p+q)^3=-113, B=-(p+3q)(p-q)^3=10185615. 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 20:02:06 UTC · history