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

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 poin...

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Bibliographic Details
Published in:arXiv.org 2017-07
Main Author: Kronberg, Max
Format: Article
Language:English
Subjects:
Division
Jacobians
Online Access:Get full text
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Summary: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.
ISSN:2331-8422