Let $J$ be the Jacobian of a curve of the form $y^\ell = f(t)$ over a finite field $\mathbb{F}_q$ (with $f(t)$ irreducible, and $\ell$ coprime to each of $q$ and $\deg(f)$). In this talk we will discuss upper and lower bounds on the size of the $\ell$-torsion in $J(\mathbb{F}_q)$ involving certain polynomial congruence conditions. For instance, we give a criterion under which the $\ell$-rank of $J(\mathbb{F}_q)$ is at least $3$, and when $\ell\leq 5$ we compute the $\ell$-rank exactly in terms of congruence conditions. This is joint work with Wanlin Li and Eric Stubley.