Mazur module for elliptic curves

Under certain assumptions parameters of the Mazur module for an elliptic curve $E$ over a $\Gamma$ extension $K_\infty/K_0$ are computed. This makes it possible, in particular, to prove in certain cases that the group $E(K_\infty)$ is finitely generated without assuming that the groups $E(K_0)$ и $\text{Ш}(\overline{K_0}/K_0,E)$ are finite.