I would like to know whether there is any solution available on the inversion of elliptic integrals of the third kind (incomplete)?

That means that given $\Pi(n,u,m) = f(x)$, I would like to obtain $u$ as a function of $x$. Here, $m = (sin(\alpha))^2$ is the parameter and $n$ is the characteristic.

I know how to invert elliptic integrals of the first kind (incomplete), but I haven't been able to find anything useful in order to invert a general elliptic integral of the third kind (incomplete, non-circular case).

Thanks for any help!