In this talk I will introduce strongly invertible Legendrian links in the standard contact three-dimensional space. After a short presentation of the equivariant analogues of well-known theorems for both strongly invertible and Legendrian links, e.g. the equivariant Legendrian Reidemeister theorem, I will introduce the maximal equivariant Thurston-Bennequin number.

I will conclude the talk discussing some experimental results and conjectures concerning the maximal equivariant Thurston-Bennequin number.

This is joint work with Paolo Lisca (Università di Pisa).