Let $R$ be a complete discrete valuation ring, with fraction field $L$. Let $E$ be an elliptic curve over $L$, and $W$ a minimal Weierstrass model over $R$. Why is $W(R) \simeq E(L)$? We have a map $W(R) \to W(L) \to E(L)$, and my question is why is it surjective. Given an $L$-point of $E$, we get an $L$-point of $W$, and how do I get an $R$-point of $W$?