2019/03/30 by Yoshinosuke Hirakawa, Hirakawa, Yoshinosuke, Hideki Matsumura +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1904.00215
openalex publication_date 2019/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.