Elliptic curves with conductor having $n$ prime factors
Volume 204 / 2022
Acta Arithmetica 204 (2022), 185-190
MSC: Primary 11G05; Secondary 11G07, 14G05.
DOI: 10.4064/aa220119-27-4
Published online: 13 June 2022
Abstract
We prove that for any integer $n \ge 2$, there are infinitely many elliptic curves over $\mathbb {Q}$ with a rational point of order 2 (resp. 3) whose conductor is a square-free integer having $n$ prime factors.
