Abstract
Let E/K be an elliptic curve defined over an imaginary quadratic field $K$ with complex multiplication by the ring of integers $R_K$ of $K$. For $\idealP$, prime of $K$ at which $E$ has good reduction, let $k_{\idealP}:=R_K/\idealP$ and $\tilde{E}/k_{\idealP}$ be the reduction of $E$ modulo $\idealP$. Our main purpose is to study the $R_K$-Module structure of$\tilde{E}(k_{\idealP})$ as $E$ to be the following two families of elliptic curves, $E_D:y^2=x^3-Dx$, $E^D:y^2=x^3+D$, for all $D\in\ZZ$.