  In our earlier articles we studied tube hypersurfaces in ${\mathbb C}^3$ that
are 2-nondegenerate and uniformly Levi degenerate of rank 1. In particular, we
showed that the vanishing of the CR-curvature of such a hypersurface is
equivalent to the Monge equation with respect to one of the variables. In the
present paper we provide an alternative shorter derivation of this equation by
utilizing two invariants discovered by S. Pocchiola. We also investigate
Pocchiola's invariants in the rigid case and give a partial classification of
rigid 2-nondegenerate uniformly Levi degenerate of rank 1 hypersurfaces with
vanishing CR-curvature.
