Multiples of integral points on Mordell curves
Volume 211 / 2023
Acta Arithmetica 211 (2023), 121-159
MSC: Primary 11G05.
DOI: 10.4064/aa220822-3-8
Published online: 16 October 2023
Abstract
Let be a sixth-power-free integer and P be a non-torsion point on the Mordell curve E_B:y^2=x^3+B. We study the integral multiples [n]P of P. Among other results, we show that P has at most three integral multiples with n \gt 1. This result is sharp in the sense that there are points P with exactly three integral multiples [n]P and n \gt 1. As an application, we discuss the number of integral points on the quasi-minimal model of rank 1 Mordell curves.
