  This paper is a sequel of arXiv:2109.06394. In this paper, we consider a kind
of inverse problem of multipliers. The problem is to count number of
isospectral correspondences, correspondences which has the same combination of
multipliers. We give a primitive explicit upper bound. In particular, for a
generic rational map of degree $d$, there are at most $O(d^{10d})$ rational
maps with the same combination of multipliers for the fixed points and the
3-periodic points. This paper also includes two proofs of a correction in the
errata of a Hutz-Tepper's result, which states that the multipliers of the
fixed and 2-periodic points determines generic cubic morphism uniquely. One is
done by proceeding the computation in Hutz-Tepper's proof. The other is done by
more explicit computation with the help of invariant theory.
