 Prime-to-characteristic geometric torsion

If $\ell$ is a prime different from the characteristic, multiplication by $\ell$ on an elliptic curve has degree ${\ell }^2$ and nonzero differential. It is a separable isogeny, so its geometric kernel has ${\ell }^2$ points, all killed by $\ell$. This gives the displayed group over an algebraic closure; the rational subgroup over the base field may be smaller.