curve #2432

y² + xy = x³ − 22871916766x + 1002886273410500

a-invariants: [1, 0, 0, -22871916766, 1002886273410500]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 5860470
discriminant (Δ): 331252162914393771326333838950400
Faltings height: 4.9501
naive height: 83.1731
primes of bad reduction: 2, 3, 5, 7, 11, 43, 59
regulator: 7.122009259140895824721294883050451541381
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:01:14 UTC
last updated: 2026-09-26 20:01:14 UTC

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

(-18724, 37752914)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-35, q=8; A=(3q-p)(p+q)^3=-1161297, B=-(p+3q)(p-q)^3=-874577. 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 20:01:15 UTC · history