  Let $\frak{p}$ and $\frak{q}$ be two distinct prime ideals of
$\mathbb{F}_q[T]$. We use the Eisenstein ideal of the Hecke algebra of the
Drinfeld modular curve $X_0(\frak{p}\frak{q})$ to compare the rational torsion
subgroup of the Jacobian $J_0(\frak{p}\frak{q})$ with its subgroup generated by
the cuspidal divisors, and to produce explicit examples of Jacquet-Langlands
isogenies. Our results are stronger than what is currently known about the
analogues of these problems over $\mathbb{Q}$.
