Let $L/K$ be finite Galois ext. of number fields and $E/K$ an elliptic curve. Define trace $$Tr : E(L) \rightarrow E(K), \;\; P \mapsto \sum_{\sigma \in G_{L/K}} P^{\sigma}$$ When is this map surjective? (Assume rk $E(K) \geq 1$).