Two dimensional neighborhoods of elliptic curves: analytic classification in the torsion case

We investigate the analytic classification of two dimensional neighborhoods of an elliptic curve with torsion normal bundle. We provide the complete analytic classification for those neighborhoods in the simplest formal class and we indicate how to generalize this construction to general torsion case.
Comment: Working version 2 (new pictures, enhanced presentation of sectorial normalization, sketch of the proof of classification in the general torsion case)