On the invariants of the quotients of the Jacobian of a curve of genus 2
Résumé
Let C be a curve of genus 2 that admits a non-hyperelliptic involution. We show that there are at most 2 isomorphism classes of elliptic curves that are quotients of degree 2 of the Jacobian of C. Our proof is constructive, and we present explicit formulae, classified according to the involutions of C, that give the minimal polynomial of the j-invariant of these curves in terms of the moduli of C. The coefficients of these minimal polynomials are given as rational functions of the moduli.
Domaines
Cryptographie et sécurité [cs.CR]
Origine : Fichiers produits par l'(les) auteur(s)