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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-1-1,
author = {Yasutsugu Fujita and Tadahisa Nara},
title = {Generators and integral points on twists of the Fermat cubic},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {1-16},
zbl = {06422679},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-1-1}
}
Yasutsugu Fujita; Tadahisa Nara. Generators and integral points on twists of the Fermat cubic. Acta Arithmetica, Tome 168 (2015) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa168-1-1/