Generators and integral points on twists of the Fermat cubic
Volume 168 / 2015
Acta Arithmetica 168 (2015), 1-16
MSC: Primary 11G05, 11D59; Secondary 11G50.
DOI: 10.4064/aa168-1-1
Abstract
We study integral points and generators on cubic twists of the Fermat cubic curve. The main results assert that integral points can be in a system of generators in the case where the Mordell–Weil rank is at most two. As a corollary, we explicitly describe the integral points on the curve.
