Groupe de torsion de courbe élliptique sur une extension quadratique de corps Q

Abstract

This paper is a survey concerning the torsion groups of elliptic curves over quadratic Fields. One starts with a preview on the Abelian varieties. Then one exposes arithmetic and geometric generalities on the elliptic curves. Then we establish the structure of Abelian group of Mordell-Weil, one is interested in the points of finite order, the subgroup of m - torsion E (K)[m] and the group of torsion T(E). One also gives two me thods of survey of these T(E groups) (K), for K =¥( d ) Method of Kamieny [8] and me thod of Kenku [9].