Classification conjecture for regular homotopy classes of curves

Let $r(\alpha)$ be the integer that counts the number of rotations of the velocity vector along a curve $\alpha$. Curves with $r(\alpha)=m$ include the curves $\gamma_m$ in the family indexed by integers $m$. Classification conjecture. Curves with the same value of $r(\,18ot\,)$ are regularly homotopic. This would imply that the displayed family $\gamma_m$, indexed by all integers, contains every curve up to regular homotopy; the conjecture is presented as the assumption that would complete the classification.