Abstract: We will state the general settings of holomorphic correspondences and what is known about their equidistribution properties in different cases. We will explain why the family \(\mathcal{F}_a\) of holomorphic correspondences given by

\[\left(\frac{aw-1}{w-1}\right)^2+\left(\frac{aw-1}{w-1}\right)\left(\frac{az+1}{z+1}\right)+\left(\frac{az+1}{z+1}\right)^2=3\]

is interesting, as well as check that it does not fit in any of the cases above. Finally, we will see its equidistribution properties.