The Lattice LAMBDA27

An entry from the Catalogue of Lattices, which is a joint project of
Neil J. A. Sloane, AT&T Labs-Research (njas@research.att.com) and
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de)

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
BASE (on a different scale from rest of this file)
GRAM
PROPERTIES
NOTES
MINIMAL_NORM
DET
KISS
LAST_LINE

NAME
LAMBDA27

DIMENSION
27

BASE (on a different scale from rest of this file)
27 32
8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 2 2 0 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 0 0 2 2 0 0 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 2 0 2 0 0 2 2 2 0 0 0 0 0 0 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0
2 0 0 2 2 2 0 0 2 0 2 0 0 0 0 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
2 2 0 0 2 0 2 0 2 0 0 2 0 0 0 0 2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0
0 2 2 2 2 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 2 2 0 0 2 2 0 0 2 2 0 0 2 2 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0
-3 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0
2 2 -2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 -2 2 0 0 0 0
4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0
2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 0 0 0 0

GRAM
27 27
16 8 8 8 8 8 8 4 8 8 8 4 8 4 4 4
8 4 4 4 0 0 0 -6 4 8 4
8 8 4 4 4 4 4 4 4 4 4 4 4 4 2 2
4 2 2 4 2 0 0 -2 4 4 4
8 4 8 4 4 4 4 4 4 4 4 4 4 2 4 2
4 4 2 2 2 0 0 -2 0 4 4
8 4 4 8 4 4 4 4 4 4 4 4 4 2 2 4
4 2 4 2 2 0 0 -2 4 4 4
8 4 4 4 8 4 4 4 4 4 4 2 4 4 4 4
4 4 4 4 2 0 0 -2 2 4 2
8 4 4 4 4 8 4 4 4 4 4 2 4 4 2 2
4 2 4 2 0 0 0 -2 2 4 2
8 4 4 4 4 4 8 4 4 4 4 2 4 2 4 2
4 2 2 4 0 0 0 -2 2 4 2
4 4 4 4 4 4 4 8 2 2 2 4 2 4 4 4
2 4 4 4 4 0 0 2 2 2 4
8 4 4 4 4 4 4 2 8 4 4 4 4 4 4 4
4 4 4 4 2 2 2 -2 2 4 2
8 4 4 4 4 4 4 2 4 8 4 4 4 4 2 2
4 4 2 2 0 2 0 -2 2 4 2
8 4 4 4 4 4 4 2 4 4 8 4 4 2 4 2
4 2 4 2 0 0 2 -2 2 4 2
4 4 4 4 2 2 2 4 4 4 4 8 2 4 4 4
2 4 4 4 4 2 2 2 2 2 4
8 4 4 4 4 4 4 2 4 4 4 2 8 4 4 4
4 2 2 2 2 2 2 -2 2 4 2
4 4 2 2 4 4 2 4 4 4 2 4 4 8 4 4
2 4 4 4 4 4 2 2 2 2 2
4 2 4 2 4 2 4 4 4 2 4 4 4 4 8 4
2 4 4 4 4 2 4 2 0 2 2
4 2 2 4 4 2 2 4 4 2 2 4 4 4 4 8
2 4 4 4 4 2 2 2 2 2 2
8 4 4 4 4 4 4 2 4 4 4 2 4 2 2 2
8 4 4 4 2 2 2 -2 2 4 2
4 2 4 2 4 2 2 4 4 4 2 4 2 4 4 4
4 8 4 4 4 4 2 2 0 2 2
4 2 2 4 4 4 2 4 4 2 4 4 2 4 4 4
4 4 8 4 4 2 4 2 2 2 2
4 4 2 2 4 2 4 4 4 2 2 4 2 4 4 4
4 4 4 8 4 2 2 2 2 2 2
0 2 2 2 2 0 0 4 2 0 0 4 2 4 4 4
2 4 4 4 8 4 4 4 1 0 3
0 0 0 0 0 0 0 0 2 2 0 2 2 4 2 2
2 4 2 2 4 8 4 4 0 0 0
0 0 0 0 0 0 0 0 2 0 2 2 2 2 4 2
2 2 4 2 4 4 8 4 0 0 0
-6 -2 -2 -2 -2 -2 -2 2 -2 -2 -2 2 -2 2 2 2
-2 2 2 2 4 4 4 8 -1 -3 0
4 4 0 4 2 2 2 2 2 2 2 2 2 2 0 2
2 0 2 2 1 0 0 -1 8 4 4
8 4 4 4 4 4 4 2 4 4 4 2 4 2 2 2
4 2 2 2 0 0 0 -3 4 8 4
4 4 4 4 2 2 2 4 2 2 2 4 2 2 2 2
2 2 2 2 3 0 0 0 4 4 8

PROPERTIES
INTEGRAL =1

NOTES
A laminated lattice LAMBDA27, constructed as in Sect. 7, Chap. 6 of SPLAG,
at scale at which it is integral.

MINIMAL_NORM
8

DET
536870912

KISS
197142

LAST_LINE

INDEX FILE | ABBREVIATIONS

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