Sorry for my bad English.
Let $X$ be elliptic curve over algebraic closed field $k$, and $P_0\in X$.
By Hartshorne's Algebraic geometry, linear system $|2P_0|$ define morphism $f:X\to \mathbb{P}^1$such that degree$f=2$.
By Hartshorne, $f$ ramify at $P_0$. But I can't understand, help me.