curve #2352

y² + xy = x³ − 483139718041x + 129167680845944825

a-invariants: [1, 0, 0, -483139718041, 129167680845944825]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 330419310
discriminant (Δ): 10071881356790838993151797899726400
Faltings height: 5.4542
naive height: 92.3243
primes of bad reduction: 2, 3, 5, 13, 17, 19, 43, 61
regulator: 3.209600871870923965437988512130301728185
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:14 UTC
last updated: 2026-09-26 19:56:14 UTC

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

(-2330893/4, 3693022183/8)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=26; A=(3q-p)(p+q)^3=69255, B=-(p+3q)(p-q)^3=4849927. 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 19:56:14 UTC · history