I'm reading [Luca De Feo's slides][1]; on the slide 12 it's written that the multiplication map $[m] : E \rightarrow E$ is an isogeny. I do not understand why this isogeny is non-cyclic. At the first glance, there would be a point of order $m$, which generates all other points in the kernel.

Furthermore, I do not understand the following: if the degree of such an isogeny would be $m^2$, does it mean that such isogeny is inseparable? Let's, for instance, take the curve $E: y^2 = x^3 + x + 4$ over $\mathbb{F}_5$. There are $9$ points on this curve. Let's take the map $P \mapsto 4P$. Obviously, $E[4] = \{\mathcal{O}\}$. What is the degree of an isogeny in this case? 


  [1]: https://defeo.lu/docet/assets/slides/2019-09-16-birmingham.pdf