  The quantized magnetic flux $\Phi=-4\pi N\sk, N=0,\pm1,...$ of
non-topological vortices in the non-relativistic Chern-Simons theory is related
to the topological degree of the $S^2\to S^2$ mapping defined by lifting the
problem to the Riemann spheres. Regular solutions with finite degree only arise
for rational functions, whose topological degree, $N$, is the commun number of
their zeros and poles on the Riemann sphere, also called their algebraic order.
