Fast computation of isomorphisms of hyperelliptic curves and 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.

References in corpus (1)

• Fields of moduli and fields of definition of curves

Cited by in corpus (8)

• Bielliptic curves of genus 3 in the hyperelliptic moduli
• Conductor and discriminant of Picard curves
• Reconstructing plane quartics from their invariants
• Computing twists of hyperelliptic curves
• Numerical computation of endomorphism rings
• On explicit descent of marked curves and maps
• The geometry of some parameterizations and encodings
• Automorphisms of Abelian Varieties and Principal Polarizations