  We provide an explicit presentation of the equivariant cohomology ring of the
compactified Jacobian $J_{q/p}$ of the rational curve $C_{q/p}$ with planar
equation $x^{q}=y^{p}$ for $(p,q)=1$. We also prove analogous results for the
closely related affine Springer fiber $Sp_{q/p}$ in the affine flag variety of
$SL_{p}$. We show that the perverse filtration on the cohomology of $J_{q/p}$
is multiplicative, and the associated graded ring under the perverse filtration
is a degeneration of the ring of functions on a moduli space of maps
$\mathbb{P}^{1}\to C_{q/p}$. We also propose several conjectures about
$J_{q/p}$ and more general compactified Jacobians.
