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Constructing Superelliptic Curves with non-trivial rational Torsion on their Jacobians (1707.04042v1)
Published 13 Jul 2017 in math.NT
Abstract: In this paper, we describe the construction of superelliptic curves with a rational point of prescribed order on their jacobians. The construction is based on Hensel's Lemma and produces for a given integer $N$ a superelliptic curve of genus linear in $N$ with a rational $N$-division point on the jacobian. The method is illustrated with multiple examples.