Infinitely many hyperelliptic curves with exactly two rational points
Number Theory
2019-04-03 v2
Abstract
In this paper, we construct some families of infinitely many hyperelliptic curves of genus with exactly two rational points. In the proof, we first show that the Mordell-Weil ranks of these hyperelliptic curves are and then determine the sets of rational points by using the Lutz-Nagell type theorem for hyperelliptic curves which was proven by Grant.
Cite
@article{arxiv.1904.00215,
title = {Infinitely many hyperelliptic curves with exactly two rational points},
author = {Yoshinosuke Hirakawa and Hideki Matsumura},
journal= {arXiv preprint arXiv:1904.00215},
year = {2019}
}
Comments
25 pages