  In this paper we study rank two commuting ordinary differential operators
with polynomial coefficients and the orbit space of the automorphisms group of
the first Weyl algebra on such operators. We prove that for arbitrary fixed
spectral curve of genus one the space of orbits is infinite. Moreover, we prove
in this case that for for any $n\ge 1$ there is a pair of self-adjoint
commuting ordinary differential operators of rank two
$L_4=(\partial_x^2+V(x))^2+W(x)$, $L_{6}$, where $W(x),V(x)$ are polynomials of
degree $n$ and $n+2$. We also prove that there are hyperelliptic spectral
curves with the infinite spaces of orbits.
