$E(\mathbb{F}_q)$ is a torsion group where $E$ is an elliptic curve?

Question

Let $E$ be an elliptic curve defined over $\mathbb{F}_q$ with $q=p^n$, then how to deduce $E(\mathbb{F}_q)$ is a torsion group?

In other words, for any $\mathbb{F}_q$-rational point $P$, why does there exist $m\geq1$ such that $[m]P=0$?

Thanks in advance.

Answer 1

The group is necessarily finite, hence torsion.