Computations of cyclotomic lattices

Abstract

We study even modular lattices having level $\ell$ and dimension $2(p-\nobreak 1)$, for p prime, and arising from the ideal class group of the p-th cyclotomic extension of $\Q(\sqrt{-\ell})$. After giving the basic theory we concentrate on Galois-invariant ideals, obtain computational results on minimal vectors and isometries, and identify several old or new extremal lattices.