Computations of Cyclotomic Lattices

Christian Batut Heinz-Georg Quebbemann Rudolf Scharlau

Abstract

We study even modular lattices having level l and dimension 2(p−1), for p prime, and arising from the ideal class group of the p-th cyclotomic extension of ℚ(\sqrt{−l}). 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.