An explicit family of cubic number fields with large 2-rank of the class group
Volume 182 / 2018
Acta Arithmetica 182 (2018), 117-132
MSC: Primary 11R29; Secondary 11G30, 14J26.
DOI: 10.4064/aa8669-10-2017
Published online: 28 December 2017
Abstract
We show how to construct infinite families of explicitly determined cubic number fields whose class group has a subgroup isomorphic to $(\mathbb{Z}/2)^8$ using degree $1$ del Pezzo surfaces. We illustrate the method and provide an example of such a family.
