curve #2463

y² + xy = x³ − 10938792530x + 440199389424900

a-invariants: [1, 0, 0, -10938792530, 440199389424900]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 720390
discriminant (Δ): 58561925617601384546304000000
Faltings height: 4.4831
naive height: 80.9603
primes of bad reduction: 2, 3, 5, 11, 37, 59
regulator: 3.689412024540699246080539740952396765644
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:03:08 UTC
last updated: 2026-09-26 20:03:08 UTC

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

(-99380, 23411710)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-11, q=16; A=(3q-p)(p+q)^3=7375, B=-(p+3q)(p-q)^3=728271. 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 20:03:08 UTC · history