  We classify the ODEs that correspond to elliptic CR-manifolds with maximal
isotropy. It follows that the dimension of the isotropy group of an elliptic
CR-manifold can be only 10 (for the quadric), 4 (for the listed examples) or
less. This is in contrast with the situation of hyperbolic CR-manifolds, where
the dimension can be 10 (for the quadric), 6 or 5 (for semi-quadrics) or less
than 4. We also prove that, for all elliptic CR-manifolds with non-linearizable
istropy group, except for two special manifolds, the points with
non-linearizable isotropy form exactly some complex curve on the manifold.
