Fast computation of isomorphisms of hyperelliptic curves and explicit descent

Reynald Lercier (1) , Christophe Ritzenthaler (2) , Jeroen Sijsling (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 IML - Institut de mathématiques de Luminy

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.

Mots clés: isomorphism; moduli; invariants; Galois descent; covariants; hyperelliptic curves; binary forms; algorithm

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Reynald Lercier, Christophe Ritzenthaler, Jeroen Sijsling. Fast computation of isomorphisms of hyperelliptic curves and explicit descent. ANTS-X, Jul 2012, San Diego, United States. pp.463-486, ⟨10.2140/obs.2013.1.463⟩. ⟨hal-00694117⟩