The Lattice LAMBDA19
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwthaachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:18:57 CEST 2014
INDEX FILE 
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
DIVISORS
HERMITE_NUMBER
BASIS
TRIANGULAR_BASIS
GRAM
NOTES
REFERENCES
LAST_LINE

NAME
LAMBDA19

DIMENSION
19

DET
128

MINIMAL_NORM
4

KISSING_NUMBER
10668

DIVISORS
2^4*8

HERMITE_NUMBER
.309851928453E+01

BASIS
19 24
.000000000000E+00 .000000000000E+00 .400000000000E+01
.400000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .400000000000E+01 .400000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .400000000000E+01
.400000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.400000000000E+01 .400000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.400000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .400000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .200000000000E+01
.200000000000E+01 .200000000000E+01 .200000000000E+01
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.400000000000E+01 .400000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .400000000000E+01
.400000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .400000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .400000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.200000000000E+01 .200000000000E+01 .200000000000E+01
.200000000000E+01 .200000000000E+01 .200000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .400000000000E+01 .400000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.400000000000E+01 .400000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .200000000000E+01
.200000000000E+01 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.000000000000E+00 .000000000000E+00 .200000000000E+01
.200000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.000000000000E+00 .000000000000E+00 .200000000000E+01
.200000000000E+01 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.000000000000E+00 .000000000000E+00 .200000000000E+01
.200000000000E+01 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.000000000000E+00 .000000000000E+00 .200000000000E+01
.200000000000E+01 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .000000000000E+00 .200000000000E+01
.000000000000E+00 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .000000000000E+00
.200000000000E+01 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .200000000000E+01
.200000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .000000000000E+00
.200000000000E+01 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .200000000000E+01
.200000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00

TRIANGULAR_BASIS
19 19
.200000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.100000000000E+01 .173205080757E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .115470053838E+01 .163299316186E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .115470053838E+01 .816496580928E+00
.141421356237E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.141421356237E+01 .141421356237E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .122474487139E+01
.707106781187E+00 .707106781187E+00 .122474487139E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .163299316186E+01
.115470053838E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .163299316186E+01
.577350269190E+00 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .141421356237E+01 .362597321469E15
.512790049702E15 .888178419700E15 .141421356237E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .707106781187E+00 .122474487139E+01
.000000000000E+00 .000000000000E+00 .707106781187E+00
.122474487139E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.163299316186E+01 .115470053838E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.163299316186E+01 .577350269190E+00 .100000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .577350269190E+00 .816496580928E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 .628036983474E15
.816496580928E+00 .577350269190E+00 .666133814775E15
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.500000000000E+00 .288675134595E+00 .816496580928E+00
.314018491737E15 .314018491737E15 .362597321469E15
.866025403784E+00 .500000000000E+00 .314018491737E15
.816496580928E+00 .288675134595E+00 .500000000000E+00
.500000000000E+00 .866025403784E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.500000000000E+00 .288675134595E+00 .816496580928E+00
.314018491737E15 .314018491737E15 .816496580928E+00
.288675134595E+00 .500000000000E+00 .314018491737E15
.816496580928E+00 .288675134595E+00 .500000000000E+00
.500000000000E+00 .288675134595E+00 .816496580928E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.000000000000E+00 .577350269190E+00 .408248290464E+00
.707106781187E+00 .707106781187E+00 .408248290464E+00
.577350269190E+00 .222044604925E15 .707106781187E+00
.408248290464E+00 .577350269190E+00 .222044604925E15
.277555756156E15 .577350269190E+00 .408248290464E+00
.707106781187E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00
.500000000000E+00 .288675134595E+00 .408248290464E+00
.707106781187E+00 .707106781187E+00 .408248290464E+00
.288675134595E+00 .500000000000E+00 .314018491737E15
.181298660735E15 .256395024851E15 .100000000000E+01
.155431223448E14 .384592537277E15 .407921986653E15
.314018491737E15 .100000000000E+01 .000000000000E+00
.000000000000E+00
.000000000000E+00 .577350269190E+00 .408248290464E+00
.707106781187E+00 .707106781187E+00 .408248290464E+00
.288675134595E+00 .500000000000E+00 .628036983474E15
.362597321469E15 .866025403784E+00 .500000000000E+00
.199840144433E14 .448691293489E15 .271947991102E15
.314018491737E15 .500000000000E+00 .866025403784E+00
.000000000000E+00
.000000000000E+00 .577350269190E+00 .408248290464E+00
.707106781187E+00 .707106781187E+00 .408248290464E+00
.288675134595E+00 .500000000000E+00 .628036983474E15
.816496580928E+00 .288675134595E+00 .500000000000E+00
.155431223448E14 .256395024851E15 .000000000000E+00
.628036983474E15 .500000000000E+00 .288675134595E+00
.816496580928E+00

GRAM
19 0
4
2 4
0 2 4
0 2 0 4
0 0 2 0 4
2 2 0 0 0 4
0 0 0 0 0 2 4
0 0 0 0 0 0 2 4
0 0 0 0 1 1 0 0 4
0 0 0 0 1 0 0 0 0 4
0 0 0 0 0 0 0 0 2 0 4
0 0 0 0 0 0 0 0 0 0 2 4
1 0 1 1 1 0 0 1 1 1 0 1 4
1 1 1 1 0 0 1 0 1 1 1 1 0 4
0 0 0 0 0 0 0 0 0 1 0 0 0 1 4
0 0 0 0 0 0 0 0 1 1 0 0 1 1 0 4
0 0 1 0 2 0 0 0 0 0 0 1 0 0 0 0 4
1 0 0 1 0 0 1 0 1 0 1 1 1 0 0 0 1 4
0 0 0 1 0 1 0 1 0 0 0 0 1 1 1 0 1 0 4

NOTES
A laminated lattice.

REFERENCES
1. SPLAG p. 157.
2. W.Plesken, M.Pohst, Constructing integral lattices with prescribed minimum II,
Math. Comp. Vol 60, N. 202 (1993) 817825

LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe