  Let $\rho$ be a mod $\ell$ Galois representation. We show how to compute
$\rho$, given the characteristic polynomial of the image of the Frobenius at
one prime $p$ and a curve $C$ whose Jacobian contains $\rho$ in its
$\ell$-torsion. The main ingredient is a method to $p$-adically lift torsion
points on a Jacobian in the framework of Makdisi's algorithms.
