This table was originally created by Michael Juergens during his dissertation project as: Extremal lattices It is maintained and updated here by Gabriele Nebe.
Keywords: modular lattices, tables, minimal norm, quadratic forms
Part of the Catalogue of Lattices which is a joint project of Gabriele Nebe, RWTH Aachen university (nebe@math.rwth-aachen.de) and Neil J. A. Sloane, (njasloane@gmail.com).
A strongly N-modular lattice is an even lattice of even level N which is similar to all its partial dual lattices. Extremal strongly modular lattices are those lattices of square free level N with divisor sum dividing 24 for which the minimum is as high as the theory of modular forms allows it to be, for a precise definition see Quebbemann, H.-G. Atkin-Lehner eigenforms and strongly modular lattices. Enseign. Math. (2) 43 (1997).
2 | 3 | 5 | 6a | 6b | 7 | 11 | 14 | 15 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|
2 | - | 1 | - | - | - | 1 | 1 | - | - | 1 |
4 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
6 | - | 1 | - | - | - | 1 | 1 | - | - | - |
8 | 1 | 2 | 1 | 1 | 1 | 1 | 1 | 2 | - | |
10 | - | 3 | - | - | - | 4 | 2 | - | - | - |
12 | 3 | 1 | 4 | 6 | 4 | 0 | 0 | 1 | 3 (5) | - |
14 | - | 1 | - | - | - | 1 | ? | - | - | - |
16 | 1 | 6 | 1 | 8 | ≥ 18 | - | ? | ≥ 1 | - | |
18 | - | 37 | - | - | - | 0 | ? | - | - | - |
20 | 3 | ≥ 100 | ≥ 72 | ? | ≥ 13 | ≥ 1 | - | ? | ? | - |
22 | - | ≥ 1000 | - | - | - | ? | ? | - | - | - |
24 | ≥ 8 | ≥ 1 | ≥ 1 | ≥ 2 | 0 | - | ? | ? | - | |
26 | - | ≥ 6 | - | - | - | ? | - | - | - | - |
28 | ≥ 24 | ≥ 9 | ≥ 1 | ? | ? | ? | - | ? | ? | - |
30 | - | ≥ 2 | - | - | - | - | - | - | - | - |
32 | ≥ 7 | ≥ 33 | ? | ? | ? | - | - | - | - | |
34 | - | ≥ 100 | - | - | - | ? | - | - | - | - |
36 | ≥ 3 | ? | ? | ? | ? | - | - | - | - | - |
38 | - | ? | - | - | - | ? | - | - | - | - |
40 | ≥ 6 | ≥ 1 | ? | ? | ? | - | - | - | - | |
42 | - | ? | - | - | - | - | - | - | - | - |
44 | ≥ 1 | ? | ? | ? | ? | - | - | - | - | - |
46 | - | ? | - | - | - | ? | - | - | - | - |
48 | ≥ 6 | ? | ? | ? | - | - | - | - | - |