Let $K$ be a number field and $E/K$ be an elliptic curve defined over $K$. Consider the localization map
$$
E(K)\otimes \mathbb{Q}_p/ \mathbb{Z}_p \rightarrow \bigoplus_{v|p} E(K_v)\otimes \mathbb{Q}_p/ \mathbb{Z}_p.
$$
Can we say when is the above map injective?