Fast computation of isomorphisms of hyperelliptic curves and explicit Galois descent

TL;DR

This paper presents a method to accelerate the computation of hyperelliptic curve isomorphisms using covariants and explores models over their field of moduli with new theoretical and practical insights.

Contribution

It introduces a faster algorithm for hyperelliptic curve isomorphisms and provides new results on models over the field of moduli.

Findings

Improved computational speed for hyperelliptic curve isomorphisms

New theoretical results on models over the field of moduli

Practical methods for explicit Galois descent

Abstract

We show how to speed up the computation of isomorphisms of hyperelliptic curves by using covariants. We also obtain new theoretical and practical results concerning models of these curves over their field of moduli.