CLASSIFICATION OF INTEGRAL LATTICES WITH LARGE CLASS NUMBER

A detailed exposition of Kneser's neighbour method for quadratic latti ces over totally real number fields, and of the sub-procedures needed for its implementation, is given. Using an actual computer program whi ch automatically generates representatives for all isomorphism classes in one genus of rational lattices, various results about genera of l- elementary lattices, for small prime level l, are obtained. For instan ce, the class number of 12-dimensional 7-elementary even lattices of d eterminant 7(6) is 395; no extremal lattice in the sense of Quebbemann exists. The implementation incorporates as essential parts previous p rograms of W. Plesken and B. Souvignier.