If $K$ is a number field, $E$ an elliptic curve and $p$ a prime, does the Selmer group
$$H^{1}_{\operatorname{Sel}}\left(K,E_{p^{n}}\right)$$
always inject into
$$\prod_{q \text{ a nonarchimedean prime of }K}H^1 \left(K_{q},E_{p^{n}}\right)$$
(Excuse me if that question is stupid)