Equations of curves with minimal discriminant

TL;DR

This paper presents an algorithm to find Weierstrass equations with minimal discriminant for superelliptic curves, extending previous methods used for elliptic and genus 2 curves.

Contribution

It generalizes Tate's and Liu's algorithms to a broader class of superelliptic curves, providing a systematic way to minimize discriminants.

Findings

Algorithm successfully computes minimal discriminant equations.

Extends existing methods from elliptic and genus 2 curves to superelliptic curves.

Enhances understanding of curve minimal models.

Abstract

In this paper we give an algorithm of how to determine a Weierstrass equation with minimal discriminant for superelliptic curves generalizing work of Tate for elliptic curves and Liu for genus 2 curves.