curve #2449

y² + xy + y = x³ − 8723280189x − 106732902094364

a-invariants: [1, 0, 1, -8723280189, -106732902094364]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 72773610
discriminant (Δ): 37562177867449840292053893536100
Faltings height: 4.7509
naive height: 80.2814
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 61
regulator: 3.444494218364111312826011632332972352482
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:17 UTC
last updated: 2026-09-26 20:02:17 UTC

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

(-76297, 10747308)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-2, q=21; A=(3q-p)(p+q)^3=445835, B=-(p+3q)(p-q)^3=742187. 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 20:02:17 UTC · history