Behavior of Arithmetic Invariants for a Class of Elliptic Curves in Cyclotomic $\Gamma$-Extensions

We study the behavior of the main arithmetic invariants of elliptic curves with complex multiplication in cyclotomic $\Gamma$-extensions. We consider the curves of CM-type which are defined over the field of rational numbers and possess nondegenerate nonsupersingular reduction modulo a prime $p$, where $p\ne 2$.