This is the introductory lecture to a mini-course (joint with Eugenia Rosu) about complex multiplication, at the CIRM Spring School 2023. It gives an overview of the basic theory of elliptic functions.

A quasi logistic distribution on the real line has density proportional to $(cosh x+cos a)^{-1}$ if $V> 0$ and $Z$ with standard normal law are independent, we say that $\sqrt{V}$ has a quasi Kolmogorov distribution if $Z\sqrt{V}$ is quasi logistic. We study the numerous properties of these generalizations of the logistic and Kolmogorov laws.