I would like to rephrase a question I asked three days ago and was closed for the unclear presentation. 

Taking T \in E[p], a point in the p-torsion of the elliptic curve and looking at the right action of SL_2(Z/pZ) on T for prime p, one can easily see that you obtain again all points in E[p] equally many times. The action is described as follows: 

(m/p \tau+n/p) (a b c d)= ((ma+nc)/p \tau+(mb+nd)\p)


Now what would happen when we take T \in E[n] where n is an integer and look at the right action of SL_2(Z/nZ)?   Do we also get again all the points in E[n] equally many times?  If not, why?