  The most general vortex solution of the Liouville equation (which arises in
non-relativistic Chern-Simons theory) is associated with rational functions,
$f(z)=P(z)/Q(z)$ where $P(z)$ and $Q(z)$ are both polynomials, $\deg P<\deg
Q\equiv N$. This allows us to prove that the solution depends on $4N$
parameters without the use of an index theorem, as well as the flux
quantization~: $\Phi=-4N\pi(sign \kappa)$.
