  The aim of this article is to give some numerical data related to the order
of the Selmer groups in twist families of elliptic curves. To do this we assume
the Birch and Swinnerton-Dyer conjecture is true and we use a celebrated
theorem of Waldspurger to get a fast algorithm to compute $% L_{E}(1)$. Having
an extensive amount of data we compare the distribution of the order of the
Selmer groups by functions of type $\alpha \frac{(\log \log
(X))^{1+\varepsilon}}{\log (X)}$ with $\varepsilon $ small. We discuss how the
"best choice" of $\alpha $ is depending on the conductor of the chosen elliptic
curves and the congruence classes of twist factors.
