This MAGMA Code can compute simple factors including multiplicity of an abelian variety over a finite field given it's L-Polynomial (i.e., the nominator of the Hasse-Weil-zeta function). Furthermore, we provide an algorithm that compute the L-Polynomial of Jacobians, associated to curves that correspond to certain Carlitz-Cyclotomic field extensions.
A rather detailed explanation of the theory underlying this algorithm can be read in my bachelor's thesis.
Also note that the code itself is by no means optimized nor sufficiently documented - try to understand at your own risk.