Argyres and collaborators have given a nice and explicit classification of 4d $\mathcal{N}=2$ SCFTs at rank one. Most of those theories are engineered by class-$S$ theory with irregular singularities. In this talk, I will give a universal formula for the rank of theory so that a complete search is possible. Various physical quantities of those theories, such as the central charges, flavor symmetry, associated vertex operator algebra and Higgs branch, etc can be computed. One of interesting consequence of our results is the prediction of many new isomorphism of vertex operator algebra. This talk will be based on the joint work with Dan Xie and Wenbin Yan.