Fast computation of isomorphisms of hyperelliptic curves and explicit   Galois descent
  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. 
Reynald Lercier and Christophe Ritzenthaler and Jeroen Sijsling
math.AG math.NT