  In this paper, we make a study of the Iwasawa theory of an elliptic curve at
a supersingular prime p along an arbitrary Z_p-extension of a number field K in
the case when p splits completely in K. Generalizing work of Kobayashi and
Perrin-Riou, we define restricted Selmer groups and \lambda^\pm,
\mu^\pm-invariants; we then derive asymptotic formulas describing the growth of
the Selmer group in terms of these invariants. To be able to work with
non-cyclotomic Z_p-extensions, a new local result is proven that gives a
complete description of the formal group of an elliptic curve at a
supersingular prime along any ramified Z_p-extension of Q_p.
