  For every odd integer $N$ we give an explicit construction of a polynomial
curve $\cC(t) = (x(t), y (t))$, where $\deg x = 3$, $\deg y = N + 1 + 2\pent
N4$ that has exactly $N$ crossing points $\cC(t_i)= \cC(s_i)$ whose parameters
satisfy $s_1 < ... < s_{N} < t_1 < ... < t_{N}$. Our proof makes use of the
theory of Stieltjes series and Pad\'e approximants. This allows us an explicit
polynomial parametrization of the torus knot $K_{2,N}$.
