Let $E$ be an elliptic curve with a $p$-torsion point. Denote this point by $P$. Why does is isogeny $\phi: E \rightarrow E/\langle P \rangle$ of degree $p$?
I do know that if $\phi$ is separable, then the degree is the order of the kernel which is $\#\langle P\rangle = p$. This gives the right answer but I'm not sure on how to show separability.