Comparing to class group cases : we have an isomorphism
$Cl(K)\rightarrow  \prod \left(K^\times \backslash K_p^\times /O_p^\times \right)$ for a number field $K$.

Similarly, for an elliptic curve $E/\mathbb{Q}$, I expect the injectivity of $Sel(E/\mathbb{Q})\rightarrow \prod \left( (E/E_{tor})(\mathbb{Q}_p)\right) \left(\hookrightarrow \prod H^1(\mathbb{Q}_p,E_{tor})\right)$, but I cannot prove or disprove it.