Computing twists of hyperelliptic curves

TL;DR

This paper presents an efficient algorithm for computing equations of twists of hyperelliptic curves of any genus over separable fields, expanding computational tools in algebraic geometry.

Contribution

It introduces a novel, efficient method for explicitly computing twists of hyperelliptic curves of arbitrary genus over various fields.

Findings

Algorithm successfully computes twists for diverse hyperelliptic curves.

Explicit examples demonstrate the method's effectiveness.

Provides a practical tool for algebraic geometry research.

Abstract

We give an efficient algorithm to compute equations of twists of hyperelliptic curves of arbitrary genus over any separable field (of characteristic different from 2), and we explicitly describe some interesting examples.