curve #2354

y² + xy + y = x³ − 360350358933x + 83122322087880556

a-invariants: [1, 0, 1, -360350358933, 83122322087880556]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 909438630
discriminant (Δ): 9881956640294710169570488688062500
Faltings height: 5.4125
naive height: 91.4446
primes of bad reduction: 2, 3, 5, 17, 23, 31, 41, 61
regulator: 5.045490517888530735133496647263014764146
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:21 UTC
last updated: 2026-09-26 19:56:21 UTC

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

(363140, 12156867)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-46, q=5; A=(3q-p)(p+q)^3=-4204181, B=-(p+3q)(p-q)^3=-4112181. 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 19:56:21 UTC · history