curve #2359

y² + xy = x³ − 211555751595x + 32661907055975025

a-invariants: [1, 0, 0, -211555751595, 32661907055975025]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 358888530
discriminant (Δ): 145116517892412866040123884001000000
Faltings height: 5.4735
naive height: 89.8469
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 37
regulator: 3.702118819269883515994056689346994499787
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:56:40 UTC
last updated: 2026-09-26 19:56:40 UTC

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

(-490740, 135515505)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-37, q=18; A=(3q-p)(p+q)^3=-624169, B=-(p+3q)(p-q)^3=2828375. 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 19:56:40 UTC · history