Infinitely many hyperelliptic curves with exactly two rational points
2021
We construct some infinite families of 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 a Lutz–Nagell type theorem for hyperelliptic curves which was proven by Grant.
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