Graph: Class Numbers of Imaginary Quadratic Fields

Posted by Jason Polak on 14. April 2014 · Write a comment · Categories: number-theory

Here’s a cool picture I made with Sage and R of class numbers of $\mathbb{Q}(\sqrt{-D})$ where $D$ is squarefree. It consists of the first five thousand such $D$ (click image to enlarge):

The even class numbers are shown in red +-signs and the odd class numbers are shown as blue disks. If you look carefully at the bottom left-hand corner where the points start, you’ll see a small conglomeration of blue dots that consist of the only nine imaginary quadratic fields that have class number one.