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arXiv · 1707.04042

Constructing Superelliptic Curves with non-trivial rational Torsion on their Jacobians

Max Kronberg
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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.

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Max Kronberg. 2017-07-13. Constructing Superelliptic Curves with non-trivial rational Torsion on their Jacobians. https://arxiv.org/abs/1707.04042

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