curve #2190

y² + xy = x³ − 551362734776020x + 4982994975317017216400

a-invariants: [1, 0, 0, -551362734776020, 4982994975317017216400]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 59213910210
discriminant (Δ): 680488820048723690403764382017093184000000
Faltings height: 7.1146
naive height: 113.4438
primes of bad reduction: 2, 3, 5, 7, 13, 19, 47, 107, 227
regulator: 5.087385694716115273470497218442050195300
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:46:01 UTC
last updated: 2026-09-26 19:46:01 UTC

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

(13744040, 1121819180)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-47, q=60; A=(3q-p)(p+q)^3=498719, B=-(p+3q)(p-q)^3=162930719. 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 19:46:01 UTC · history