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arXiv · 1904.00215

Infinitely many hyperelliptic curves with exactly two rational points

Yoshinosuke Hirakawa·Hideki Matsumura
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Abstract

In this paper, we construct some families of infinitely many hyperelliptic curves of genus $2$ with exactly two rational points. In the proof, we first show that the Mordell-Weil ranks of these hyperelliptic curves are $0$ and then determine the sets of rational points by using the Lutz-Nagell type theorem for hyperelliptic curves which was proven by Grant.

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Yoshinosuke Hirakawa, Hideki Matsumura. 2019-03-30. Infinitely many hyperelliptic curves with exactly two rational points. https://arxiv.org/abs/1904.00215

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