Why is the Class Number of $\Q(\sqrt[3]{11})$ even?

Franz Lemmermeyer

Published 2011-08-30Version 1

In this article we will describe a surprising observation that occurred in the construction of quadratic unramified extensions of a family of pure cubic number fields. Attempting to find an explanation will lead us on a magical mystery tour through the land of pure cubic number fields, Hilbert class fields, and elliptic curves.