An explicit family of cubic number fields with large $2$-rank of the class group

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.

arXiv commentWe have corrected an error in the proof of Corollary 3.9 (now Corollary 3.10). Additionally, we have made several changes to improve the readability of the paper. 19 pages