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Infinitely many hyperelliptic curves with exactly two rational points. (arXiv:1904.00215v2 [math.NT] UPDATED)
来源于:arXiv
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. 查看全文>>