Let $C$ be a fixed equisingularity class of irreducible germs of complex analytic plane curves. We compute a basis of the $\mathbb{C}[[x]]$-module of Kahler differentials for generic $Gamma\in C$. Our method is algorithmic.

As an application, we give an alternative proof for a formula of Genzmer, that provides the dimension of the moduli of analytic classes in the equisingularity class of $\Gamma$.

This is a joint work with Pedro Fortuny Ayuso.