curve #2447

y² + xy = x³ − 10130707885x + 374590335230225

a-invariants: [1, 0, 0, -10130707885, 374590335230225]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 6622770
discriminant (Δ): 5924922302495907158765625000000
Faltings height: 4.6625
naive height: 80.7301
primes of bad reduction: 2, 3, 5, 7, 11, 47, 61
regulator: 4.338117740257550983625258793751646616369
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:02:09 UTC
last updated: 2026-09-26 20:02:09 UTC

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

(1870, 18857815)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-7, q=18; A=(3q-p)(p+q)^3=81191, B=-(p+3q)(p-q)^3=734375. 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 20:02:10 UTC · history