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

Elliptic CR-manifolds and shear invariant ordinary differential equations with additional symmetries