curve #2422

y² + xy = x³ − 46581725196x + 3866180331281040

a-invariants: [1, 0, 0, -46581725196, 3866180331281040]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 4458090
discriminant (Δ): 11575724043896057805102120960000
Faltings height: 4.8783
naive height: 85.3070
primes of bad reduction: 2, 3, 5, 7, 13, 23, 71
regulator: 3.707463650814724486573928363654660847523
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:00:36 UTC
last updated: 2026-09-26 20:00:36 UTC

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

(-162664, 84575924)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-23, q=16; A=(3q-p)(p+q)^3=-24353, B=-(p+3q)(p-q)^3=1482975. 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 20:00:36 UTC · history