Computing twists of hyperelliptic curves

Davide Lombardo (1) , Elisa Lorenzo García (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: Hyperelliptic curves; Galois cohomology; Conics Twists

Domaines: Théorie des nombres [math.NT]

Davide Lombardo, Elisa Lorenzo García. Computing twists of hyperelliptic curves. Journal of Algebra, 2019, 519, pp.474-490. ⟨10.1016/j.jalgebra.2018.08.035⟩. ⟨hal-01618637⟩