Computations of Cyclotomic Lattices

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(√−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.

Keywords:

• lattice
• integral quadratic form
• Craig lattice
• hermitian lattice
• modular lattice
• extremal lattice
• isodual Hermite number
• cyclotomic ideal