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.