The Lattice hat(A)_22^(2).otimes(3).A_2
An entry from 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)
Last modified Fri Jul 18 13:12:29 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
GRAM
DIVISORS
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
SUBGROUP_ORDER
SUBGROUP_NAME
SUBGROUP_GENERATORS
PROPERTIES
REFERENCES
NOTES
LAST_LINE
-
NAME
hat(A)_22^(2).otimes(3).A_2
-
DIMENSION
44
-
GRAM
44 0
8
3 8
0 -1 8
1 1 -2 8
-1 0 4 -3 8
1 0 -2 -1 -2 8
0 0 0 2 0 -3 8
4 3 0 2 0 0 1 8
-2 0 2 -3 2 -2 1 0 8
0 2 -3 -1 -1 0 -2 0 0 8
0 -1 3 1 -1 -2 -1 0 2 -1 8
3 2 0 0 -1 1 0 4 0 -1 0 8
-2 0 1 -1 2 -2 0 -1 1 -1 2 0 8
-1 2 0 -2 3 0 -3 -1 2 3 -1 -3 -1 8
0 1 1 0 2 -1 0 0 -3 1 -2 -1 -2 1 8
1 -1 1 -2 2 2 0 -1 1 -1 1 1 2 -1 -2 8
1 -2 0 -2 -2 1 0 0 0 1 2 2 -1 -2 1 2 8
-1 1 0 -1 3 0 1 0 2 -2 -3 -1 1 2 -1 2 -3 8
2 -1 -2 -2 0 2 0 -1 -1 0 -2 0 0 0 -2 3 1 -1 8
0 0 -2 -1 0 2 1 -1 0 0 0 1 3 0 -3 3 0 1 2 8
0 -1 4 -1 1 2 0 0 1 -3 0 0 0 0 -1 1 -1 1 1 -1 8
3 3 0 -1 1 -1 2 3 1 -1 -1 3 2 -1 1 1 0 1 1 1 0 8
3 4 -1 0 -1 0 1 4 0 1 0 3 0 0 0 -1 -1 0 -1 1 0 4 8
4 4 -1 -1 0 1 -1 3 0 1 0 4 1 0 -1 2 0 1 1 2 -1 4 3 8
2 3 0 -1 -1 1 0 2 1 -1 1 3 0 -1 -1 -1 0 -1 0 1 0 4 4 2 8
3 4 1 0 0 2 -2 3 0 -1 1 4 -1 0 0 1 0 1 -2 1 0 2 3 4 4 8
0 0 -3 0 0 2 -3 -1 -3 2 0 -1 1 2 1 0 -1 -1 1 1 -1 -1 0 1 -1 0 8
0 0 2 0 3 -1 -2 -1 -2 -2 1 -1 2 1 1 1 -1 2 -1 0 -1 -1 -2 1 -1 2 1 8
0 1 -1 2 2 0 1 0 -3 0 -3 -1 1 1 0 0 -4 1 2 0 2 0 0 0 -2 -2 3 0 8
0 2 2 2 3 -2 0 1 1 0 0 -2 1 3 0 -1 -4 2 -1 0 0 0 -1 0 -1 0 -1 3 1 8
2 2 0 0 1 -1 0 2 0 -1 -1 3 1 1 0 -1 -2 1 -1 0 0 3 3 2 3 3 1 2 1 0 8
4 3 1 1 1 -1 1 4 0 -1 0 2 -1 0 2 0 0 0 0 -1 1 4 2 3 3 3 -1 0 0 1 2 8
0 -1 -2 1 -1 1 -3 -1 -4 -1 -2 0 1 -1 1 0 -1 2 0 -1 -1 0 -1 0 0 0 2 2 1 -1 1 0 8
-1 -1 1 -3 3 -2 -3 0 2 2 1 1 1 2 0 1 1 1 -2 -1 -3 -1 -1 0 -1 0 0 2 -2 0 1 -1 1 8
3 4 1 -1 0 1 -1 2 1 -1 0 4 0 0 0 1 1 1 -1 0 1 3 2 4 3 4 -1 0 -1 0 3 4 0 0 8
0 0 0 -2 0 0 2 0 -1 -3 -3 1 2 -2 -1 -1 -1 2 2 1 2 2 1 1 0 -1 0 0 2 -1 0 -1 1 -2 0 8
4 3 0 -1 0 -1 0 2 0 1 0 2 -2 1 2 -1 1 -1 0 -1 -2 3 2 2 4 3 0 1 -2 0 4 4 0 1 3 -2 8
4 3 1 0 0 -1 -1 4 0 2 1 3 -1 1 0 0 0 -2 0 0 0 2 3 3 3 3 0 -1 0 1 2 4 -1 1 3 -2 4 8
3 4 -1 1 -1 1 0 3 1 0 1 4 0 -1 0 0 0 0 -1 0 0 3 3 4 4 4 1 0 -1 0 3 4 0 -1 4 -1 3 2 8
2 4 0 -1 0 -1 0 2 1 1 0 4 1 0 0 0 0 -1 1 0 0 4 3 4 3 2 -1 0 0 1 3 3 -1 0 4 0 4 3 4 8
3 4 1 1 -1 -1 0 3 1 -1 2 4 0 -1 -1 -1 0 -1 -1 -1 1 2 3 2 4 4 0 -1 0 0 3 2 -1 -1 4 0 3 4 4 4 8
1 0 4 1 1 -3 0 0 2 1 3 -1 -1 1 1 -1 1 -3 -1 -2 1 0 -1 -1 0 0 -3 0 -2 3 -1 2 -3 0 0 -3 1 2 0 1 1 8
0 -2 -2 1 -2 -3 1 0 -1 -1 2 0 0 -2 -1 -1 2 -2 1 -1 -2 0 0 -1 1 -2 0 0 0 -3 1 0 1 1 -1 0 1 0 -1 0 1 -1 8
-1 -2 1 0 -1 -2 -1 -1 0 -1 0 0 -1 -1 -1 -2 0 0 -2 -3 0 -3 -1 -3 -1 -1 -1 -1 0 -2 0 -2 2 2 0 1 -1 0 -3 -3 1 -1 3 8
-
DIVISORS
23^6
-
MINIMAL_NORM
8
-
KISSING_NUMBER
2708112
-
HERMITE_NUMBER
5.22
-
SUBGROUP_ORDER
2^5 * 3^2 * 11 *23
-
SUBGROUP_NAME
L_2(23) otimes D_12
-
SUBGROUP_GENERATORS
2
44 44
6 -40 -8 -31 39 2 -2 -44 -51 48 -7 83 31 62 -58 33 -51 -37 -57 -64 -18 1 9 -28 -44 11 -51 -20 -30 15 -26 29 6 -56 17 33 37 -9 0 -75 45 -31 54 -84
15 -110 -26 -84 114 5 -9 -122 -145 131 -16 225 83 171 -163 93 -137 -102 -159 -177 -51 3 24 -77 -121 28 -144 -58 -84 41 -68 80 16 -156 45 96 102 -22 3 -206 124 -86 146 -231
-17 116 29 90 -124 -4 12 130 156 -139 16 -240 -88 -182 175 -100 144 107 172 189 55 -3 -24 83 128 -29 153 64 90 -44 71 -85 -16 169 -47 -103 -108 22 -3 218 -130 92 -155 246
-3 14 -7 6 -8 -3 -3 15 7 -16 10 -26 -12 -20 18 -7 17 15 15 20 7 0 -7 9 16 -7 13 3 8 -4 13 -8 -6 15 -9 -8 -12 3 1 26 -15 11 -22 31
-15 95 23 75 -102 -5 9 108 127 -115 13 -199 -73 -149 144 -80 119 87 141 156 46 -3 -20 70 107 -25 125 52 74 -36 59 -70 -14 140 -39 -84 -88 17 -2 179 -106 75 -129 203
-3 19 2 15 -23 -2 2 25 26 -26 3 -44 -15 -31 32 -16 25 18 29 34 11 -1 -5 16 24 -5 26 11 17 -8 12 -16 -4 31 -8 -18 -18 3 0 39 -23 17 -29 45
3 -20 -2 -15 26 2 -5 -28 -27 28 -4 47 16 32 -35 18 -26 -20 -33 -36 -12 0 6 -17 -27 5 -29 -13 -18 9 -12 18 4 -34 8 21 21 -3 0 -43 25 -19 32 -50
11 -90 -23 -68 94 5 -7 -99 -120 107 -11 183 68 140 -132 76 -112 -82 -129 -144 -41 3 19 -62 -99 23 -118 -48 -69 33 -55 65 12 -127 36 79 84 -18 3 -167 101 -69 118 -186
-1 5 5 6 -9 1 3 7 12 -7 -2 -13 -4 -9 10 -7 7 4 11 11 3 0 1 5 6 -1 9 6 6 -3 1 -5 1 11 -1 -7 -5 0 0 10 -5 5 -7 12
18 -123 -24 -90 124 7 -7 -134 -156 146 -21 248 93 190 -179 101 -152 -113 -174 -195 -57 4 27 -86 -133 33 -156 -62 -93 44 -78 87 19 -171 52 105 111 -24 3 -226 136 -95 163 -255
4 -19 -7 -17 20 2 -1 -21 -26 23 0 41 15 30 -27 16 -24 -15 -28 -32 -10 0 3 -15 -20 5 -25 -10 -14 7 -11 14 2 -29 7 17 16 -3 0 -34 20 -13 25 -39
4 -26 -1 -19 28 4 -1 -33 -32 34 -6 57 21 41 -41 20 -34 -25 -38 -44 -14 1 8 -20 -33 9 -34 -14 -21 10 -18 20 6 -39 12 23 25 -4 0 -52 30 -22 40 -60
3 -11 1 -8 13 2 -2 -15 -12 15 -3 26 9 17 -18 9 -14 -10 -17 -20 -8 -1 4 -10 -14 4 -14 -7 -9 5 -7 9 3 -19 5 11 10 -1 -1 -22 12 -10 19 -28
4 -35 -11 -26 33 0 -1 -34 -46 38 -4 66 25 54 -48 30 -42 -32 -48 -53 -14 1 6 -22 -34 8 -44 -17 -25 12 -21 23 4 -45 14 29 31 -8 2 -61 38 -25 41 -67
-4 12 -3 11 -12 -3 0 17 11 -17 5 -31 -11 -19 20 -8 17 11 19 22 9 1 -5 12 17 -5 14 6 9 -5 10 -10 -5 21 -7 -10 -11 1 2 26 -14 10 -23 33
4 -26 -5 -18 24 1 -1 -26 -30 30 -5 50 19 39 -35 21 -32 -24 -35 -39 -11 0 6 -17 -26 7 -32 -11 -18 8 -17 17 4 -34 12 21 23 -6 0 -46 28 -19 33 -52
12 -79 -22 -59 81 4 -5 -84 -103 92 -9 157 60 122 -112 66 -97 -71 -112 -125 -35 2 15 -54 -83 21 -102 -41 -59 28 -48 54 10 -110 32 68 71 -15 3 -142 85 -59 101 -159
-5 22 -3 15 -20 -3 -1 26 23 -28 9 -47 -19 -34 33 -15 28 21 30 36 12 0 -7 17 26 -9 25 10 17 -8 17 -16 -6 31 -11 -17 -19 4 1 42 -24 18 -34 50
6 -25 7 -17 20 2 2 -29 -22 31 -15 54 22 39 -38 17 -33 -27 -34 -40 -13 -1 10 -19 -30 11 -27 -10 -18 9 -22 17 9 -34 15 17 23 -6 -2 -50 28 -21 41 -60
11 -66 -11 -50 71 5 -8 -78 -84 82 -11 141 51 103 -101 56 -83 -61 -99 -110 -35 0 16 -50 -76 18 -87 -37 -51 26 -41 50 11 -99 28 61 62 -11 0 -127 74 -54 94 -147
-15 103 31 81 -113 -3 12 115 143 -124 9 -213 -77 -162 155 -91 128 93 154 169 49 -3 -19 74 112 -24 138 58 81 -39 60 -76 -12 152 -40 -94 -95 19 -3 192 -115 81 -135 216
21 -144 -36 -112 156 9 -13 -164 -193 175 -18 301 110 226 -218 123 -181 -133 -213 -237 -69 4 31 -104 -162 37 -191 -79 -113 55 -88 107 21 -211 58 129 135 -27 3 -272 162 -114 195 -307
24 -171 -41 -132 183 10 -16 -194 -228 207 -23 356 130 268 -258 146 -214 -158 -252 -280 -82 5 37 -123 -192 44 -226 -93 -133 65 -105 127 25 -249 69 153 160 -32 4 -323 193 -135 231 -364
8 -50 -3 -36 48 4 -2 -57 -59 61 -13 104 39 77 -74 39 -63 -47 -70 -80 -25 1 14 -36 -57 15 -62 -24 -37 18 -34 36 10 -70 23 41 46 -10 0 -95 56 -40 71 -109
16 -103 -23 -81 112 8 -9 -121 -136 127 -15 219 80 162 -158 87 -130 -96 -154 -172 -51 2 24 -76 -119 28 -137 -57 -81 41 -64 78 17 -153 42 93 97 -18 1 -198 117 -83 144 -225
12 -93 -26 -71 97 4 -8 -102 -124 110 -10 188 69 144 -136 79 -115 -85 -134 -149 -42 3 19 -64 -101 23 -123 -49 -70 34 -56 67 12 -131 37 82 86 -18 3 -172 104 -72 120 -192
5 -28 0 -19 25 1 -1 -31 -31 33 -10 57 22 43 -41 22 -34 -27 -39 -44 -14 0 8 -20 -30 9 -33 -13 -20 10 -20 20 6 -38 13 22 25 -6 -1 -52 31 -23 39 -61
-17 108 18 81 -113 -9 7 124 137 -132 20 -226 -84 -169 163 -88 136 101 157 176 53 -3 -26 79 123 -30 139 56 84 -40 70 -80 -19 156 -46 -94 -100 20 -1 205 -122 86 -150 233
6 -38 -4 -29 41 3 -3 -46 -48 48 -9 83 30 60 -60 32 -49 -37 -57 -64 -20 0 10 -29 -45 11 -49 -21 -31 15 -25 30 8 -57 17 34 36 -7 -1 -75 44 -32 56 -87
-12 73 14 55 -76 -5 5 83 93 -88 13 -151 -57 -114 109 -60 91 68 106 119 35 -2 -17 53 82 -21 94 38 56 -27 47 -53 -12 105 -31 -63 -67 13 -1 137 -81 58 -100 156
10 -75 -14 -57 82 4 -8 -89 -99 93 -13 159 57 118 -117 64 -94 -72 -112 -125 -37 2 19 -55 -88 20 -100 -42 -60 30 -47 58 13 -111 31 68 72 -14 1 -146 87 -63 105 -166
6 -51 -8 -37 51 4 -2 -57 -64 62 -10 104 39 79 -75 41 -64 -49 -71 -81 -23 2 13 -35 -58 14 -66 -25 -39 19 -33 37 9 -70 22 43 48 -11 1 -97 59 -41 69 -108
1 -10 -7 -10 15 0 -3 -13 -19 13 2 23 7 17 -18 11 -13 -9 -18 -19 -5 1 1 -8 -12 1 -16 -8 -10 5 -4 9 0 -18 3 11 10 -1 0 -20 12 -9 13 -22
-6 38 3 28 -39 -2 4 45 46 -47 11 -81 -30 -59 59 -31 48 38 56 62 19 0 -11 28 45 -11 49 20 29 -15 26 -29 -8 55 -17 -33 -37 8 0 75 -44 32 -55 86
11 -77 -14 -58 80 6 -5 -88 -98 94 -13 160 59 120 -115 63 -97 -73 -111 -125 -37 2 19 -55 -88 21 -101 -40 -59 29 -49 57 14 -110 33 67 72 -15 1 -147 88 -62 106 -166
-5 43 20 34 -46 0 4 43 63 -49 -1 -83 -30 -67 60 -39 52 37 62 67 17 -2 -5 28 42 -8 58 23 33 -15 23 -30 -2 59 -15 -39 -38 9 -3 75 -47 31 -49 81
13 -89 -22 -69 95 5 -7 -101 -119 108 -12 185 68 140 -134 76 -112 -83 -131 -146 -42 3 19 -64 -100 23 -118 -48 -70 34 -55 66 13 -129 36 79 83 -17 2 -168 101 -71 120 -189
18 -117 -21 -87 120 9 -6 -132 -148 142 -20 242 90 182 -173 95 -147 -108 -167 -189 -56 3 27 -84 -131 33 -150 -60 -90 43 -75 85 20 -166 50 101 107 -22 1 -219 131 -92 160 -249
5 -41 0 -28 40 3 -3 -49 -48 51 -14 86 32 63 -63 32 -51 -41 -58 -66 -20 1 14 -29 -49 12 -52 -20 -31 16 -29 31 9 -57 19 34 40 -9 0 -82 49 -35 60 -93
11 -73 -9 -55 77 6 -5 -86 -93 91 -16 155 57 115 -113 60 -93 -70 -107 -121 -37 2 19 -54 -86 21 -95 -39 -58 28 -48 55 14 -107 32 64 69 -14 1 -142 84 -60 105 -162
16 -105 -20 -80 110 7 -8 -121 -135 128 -18 220 81 164 -158 87 -132 -98 -153 -172 -51 2 25 -76 -119 29 -137 -56 -81 40 -67 78 18 -152 44 92 98 -20 1 -200 119 -84 145 -227
-6 41 13 33 -46 -1 6 47 57 -49 4 -86 -31 -65 63 -37 51 38 63 68 20 -1 -8 30 46 -10 56 24 32 -16 24 -31 -5 62 -16 -38 -39 7 -1 78 -46 33 -55 88
11 -67 -17 -55 75 4 -7 -79 -92 83 -8 145 53 107 -104 58 -85 -61 -102 -114 -34 1 14 -51 -77 18 -90 -39 -54 27 -41 51 10 -103 27 61 63 -11 1 -129 75 -54 94 -147
-3 24 4 17 -24 0 3 26 31 -28 6 -48 -18 -37 36 -21 29 23 35 38 11 0 -6 16 26 -6 31 13 18 -9 15 -17 -3 33 -10 -21 -23 6 -1 45 -27 19 -32 51
44 44
7 -58 -15 -44 60 3 -3 -63 -76 68 -8 116 43 90 -85 48 -72 -55 -82 -92 -25 3 13 -39 -64 15 -76 -29 -44 21 -37 41 9 -80 24 49 54 -12 2 -108 66 -45 75 -119
3 -35 -15 -28 39 1 -4 -37 -52 40 0 69 25 55 -51 32 -43 -31 -51 -56 -15 2 5 -23 -37 7 -48 -20 -28 13 -19 25 2 -50 12 32 32 -6 3 -63 39 -26 42 -68
4 -36 -6 -24 33 0 -2 -37 -43 41 -8 68 26 54 -50 29 -43 -35 -48 -54 -14 1 9 -22 -37 10 -45 -17 -25 13 -23 24 6 -45 16 29 33 -9 1 -66 40 -28 45 -73
9 -64 -21 -51 69 2 -7 -70 -88 75 -6 131 48 100 -95 56 -79 -58 -95 -104 -29 2 12 -45 -69 15 -85 -35 -49 24 -38 46 7 -93 25 57 59 -12 2 -118 71 -49 83 -132
-15 96 24 75 -105 -6 9 110 129 -117 12 -202 -74 -151 146 -82 121 88 143 159 47 -2 -20 71 108 -25 127 53 76 -36 59 -72 -14 142 -39 -87 -89 17 -1 181 -108 76 -131 206
8 -59 -9 -44 63 5 -3 -69 -76 73 -12 124 46 93 -91 48 -75 -57 -86 -97 -29 2 15 -43 -69 17 -77 -31 -47 22 -39 44 11 -85 26 52 56 -11 1 -114 68 -48 83 -129
-3 28 13 23 -35 0 5 32 44 -34 -1 -58 -20 -45 44 -27 35 26 44 47 13 -1 -4 20 31 -5 41 18 24 -11 14 -22 -2 43 -10 -28 -27 5 -2 53 -32 23 -35 58
7 -57 -15 -43 60 3 -5 -63 -75 67 -7 115 42 88 -84 48 -70 -53 -82 -91 -26 2 13 -39 -63 14 -75 -30 -43 21 -35 41 8 -80 23 50 53 -11 2 -106 64 -44 74 -118
-3 15 -6 10 -17 -3 1 23 15 -22 9 -37 -14 -24 28 -10 20 17 23 28 10 0 -8 14 23 -7 19 8 13 -7 13 -13 -6 25 -9 -13 -16 2 1 35 -19 16 -29 42
5 -35 -12 -28 41 1 -5 -40 -50 43 -2 74 26 56 -54 32 -44 -32 -54 -58 -17 1 6 -26 -39 7 -48 -20 -29 13 -20 27 4 -54 13 33 33 -6 1 -66 40 -28 46 -74
20 -135 -32 -101 139 6 -11 -148 -174 160 -20 274 102 209 -197 114 -167 -125 -194 -216 -62 2 29 -94 -146 35 -175 -71 -102 50 -83 97 20 -190 56 118 124 -27 2 -250 150 -105 178 -282
14 -108 -30 -84 117 7 -10 -122 -146 130 -11 223 81 168 -162 92 -135 -99 -158 -176 -51 4 23 -77 -121 27 -144 -59 -84 41 -65 80 15 -156 43 97 101 -20 3 -203 122 -84 143 -227
3 -10 -3 -7 7 1 1 -8 -10 10 -1 18 8 14 -10 8 -12 -7 -12 -14 -4 -1 1 -6 -7 3 -10 -4 -6 3 -6 5 1 -12 4 7 7 -2 0 -14 8 -5 11 -16
-11 68 5 48 -68 -6 4 79 80 -84 17 -142 -53 -104 102 -53 85 64 96 110 34 -1 -19 50 78 -21 85 34 51 -25 46 -50 -14 96 -31 -58 -63 13 1 130 -77 55 -97 150
-17 110 31 86 -116 -6 8 121 147 -131 12 -226 -83 -172 162 -94 138 100 161 178 51 -3 -21 78 119 -27 144 58 85 -40 67 -80 -15 158 -44 -97 -100 21 -2 202 -122 84 -144 228
-2 20 14 18 -26 2 6 21 35 -22 -4 -40 -14 -32 31 -21 23 16 33 34 9 0 -1 14 20 -3 30 15 16 -8 8 -15 1 32 -5 -21 -19 3 -2 35 -21 15 -22 39
3 -17 7 -9 14 4 1 -21 -13 23 -9 36 14 25 -25 10 -22 -18 -21 -26 -10 0 8 -13 -22 7 -19 -6 -12 6 -14 13 7 -22 10 13 16 -4 -2 -35 21 -15 28 -41
-22 153 35 115 -163 -8 15 173 200 -185 22 -316 -116 -238 229 -130 190 142 224 249 73 -3 -34 110 170 -40 201 83 118 -58 94 -113 -23 221 -63 -137 -143 29 -2 288 -172 122 -206 326
-1 13 9 11 -16 1 3 13 21 -14 -2 -25 -9 -20 19 -13 15 11 20 21 5 0 -1 8 13 -2 19 9 10 -5 5 -9 0 19 -4 -13 -12 2 -1 23 -14 9 -14 25
4 -19 -4 -15 19 4 2 -21 -23 23 -3 40 16 30 -27 15 -25 -17 -27 -31 -9 0 4 -14 -21 6 -23 -9 -15 7 -13 13 4 -27 8 16 17 -3 0 -34 20 -13 27 -39
4 -24 -11 -21 27 0 -2 -26 -36 28 0 50 18 39 -36 22 -31 -22 -37 -40 -10 1 3 -17 -25 6 -33 -14 -19 9 -14 17 2 -35 9 22 22 -5 1 -44 26 -18 30 -49
-15 98 21 76 -106 -4 10 113 130 -120 16 -207 -75 -155 151 -84 123 93 147 162 48 -2 -22 72 111 -25 130 54 77 -38 61 -74 -16 145 -41 -88 -92 19 -1 188 -112 80 -135 214
6 -46 -13 -35 49 3 -4 -51 -61 54 -5 93 35 71 -67 39 -57 -42 -66 -74 -21 1 10 -32 -51 12 -61 -25 -35 17 -28 33 6 -65 18 41 43 -8 2 -85 51 -35 60 -95
10 -79 -26 -63 88 5 -8 -89 -111 95 -5 164 59 124 -119 69 -99 -71 -117 -130 -37 3 15 -56 -88 18 -107 -44 -63 30 -46 59 9 -116 30 72 74 -14 3 -148 89 -61 103 -164
0 -7 -3 -3 7 0 -1 -6 -9 7 0 9 4 9 -8 6 -7 -6 -8 -9 -2 0 1 -3 -6 2 -9 -4 -5 2 -3 4 0 -7 2 7 6 -1 1 -10 7 -5 6 -11
9 -77 -20 -58 84 5 -7 -87 -104 93 -9 157 57 120 -116 66 -96 -72 -112 -125 -36 3 17 -54 -87 19 -103 -42 -61 29 -46 57 11 -110 31 70 72 -14 3 -145 88 -61 102 -162
9 -52 -16 -44 61 4 -5 -62 -73 65 -4 114 41 84 -82 46 -67 -48 -81 -90 -27 1 10 -41 -61 14 -71 -31 -43 21 -31 40 8 -82 21 49 49 -8 1 -100 58 -42 73 -114
-5 31 15 27 -35 -1 3 33 46 -36 -2 -64 -23 -49 45 -28 39 26 47 51 14 -1 -3 23 32 -7 42 18 24 -11 17 -22 -2 46 -11 -29 -28 5 -1 55 -33 22 -38 62
-8 59 10 41 -59 -3 4 64 73 -70 11 -117 -44 -90 85 -48 72 55 82 92 27 -1 -14 40 64 -16 75 30 44 -21 37 -42 -10 80 -25 -51 -54 12 -1 109 -66 46 -78 123
-6 32 -2 24 -36 -5 3 43 38 -44 10 -75 -27 -51 54 -25 43 32 49 57 20 0 -11 28 43 -11 42 18 27 -13 23 -27 -9 51 -16 -30 -32 5 2 68 -39 29 -53 81
0 -6 -5 -5 10 1 -2 -8 -11 7 2 12 4 9 -10 6 -7 -5 -10 -11 -3 1 1 -4 -8 1 -10 -5 -6 3 -2 5 0 -10 1 7 6 0 1 -11 7 -5 7 -12
-15 98 16 73 -101 -6 7 111 124 -119 19 -204 -76 -153 147 -81 123 92 142 159 48 -2 -23 71 110 -27 126 51 75 -36 63 -72 -17 141 -42 -85 -91 19 -1 185 -110 78 -135 211
-14 106 29 80 -110 -5 9 115 140 -125 12 -214 -79 -165 154 -91 131 97 153 169 48 -3 -21 73 114 -26 139 56 80 -39 64 -76 -14 149 -42 -94 -98 21 -3 195 -118 81 -137 218
-6 40 10 31 -43 -3 3 45 54 -48 5 -83 -31 -63 60 -34 50 36 59 66 19 -1 -8 29 44 -11 52 22 31 -15 25 -29 -5 58 -16 -36 -37 7 -1 74 -44 31 -54 84
-6 29 -1 21 -29 -1 3 35 33 -37 11 -64 -24 -46 46 -24 37 29 44 49 16 1 -9 23 34 -9 36 15 22 -11 21 -22 -7 44 -14 -25 -28 6 1 58 -33 25 -45 69
-4 35 11 25 -38 0 5 38 47 -41 4 -69 -25 -54 51 -31 42 33 51 55 15 -1 -7 23 37 -7 47 19 27 -13 20 -25 -4 49 -14 -32 -33 7 -1 65 -40 28 -44 72
-5 26 10 22 -27 -1 2 27 36 -30 1 -54 -20 -41 37 -23 33 22 39 42 12 0 -3 19 26 -6 34 14 19 -9 15 -18 -2 38 -10 -23 -23 5 -1 46 -27 18 -33 52
6 -49 -21 -40 56 1 -6 -54 -71 58 0 100 35 77 -73 45 -61 -45 -74 -80 -21 2 8 -34 -53 10 -68 -28 -39 19 -27 36 5 -72 18 46 46 -9 2 -91 55 -38 61 -100
1 -17 -12 -14 20 0 -2 -16 -27 18 3 31 11 26 -23 16 -20 -14 -24 -26 -6 1 1 -10 -16 3 -24 -10 -13 6 -8 11 0 -23 5 16 15 -3 2 -28 18 -11 17 -29
-3 15 0 11 -14 0 0 16 17 -18 6 -31 -12 -24 23 -12 19 16 22 24 7 0 -4 11 17 -5 18 7 11 -5 11 -10 -4 21 -8 -12 -14 4 0 29 -17 12 -22 34
11 -83 -27 -65 90 4 -8 -91 -114 98 -5 168 61 129 -122 72 -103 -75 -121 -134 -38 3 15 -58 -90 20 -111 -46 -64 31 -48 60 10 -119 32 75 76 -15 3 -152 92 -64 106 -170
11 -87 -27 -65 90 2 -8 -91 -116 101 -8 171 63 134 -124 75 -106 -79 -124 -136 -37 3 16 -58 -90 20 -114 -45 -65 31 -51 61 10 -120 34 76 79 -18 3 -157 96 -66 108 -174
-9 75 19 57 -77 -3 4 81 99 -88 11 -151 -56 -117 110 -63 93 70 107 119 33 -3 -16 51 81 -19 97 38 57 -27 47 -53 -11 104 -31 -64 -69 15 -3 139 -84 57 -97 154
-3 21 -1 13 -18 -3 -1 23 21 -25 8 -42 -17 -32 29 -15 26 20 27 32 10 0 -7 14 23 -7 24 8 15 -7 16 -14 -5 27 -10 -16 -19 4 0 39 -23 16 -30 44
-
PROPERTIES
-
REFERENCES
T. Shioda, Mordell-Weil lattices and sphere packings,
Amer. J. Math. 113 (1991), 931-948.
G. Nebe, Some cyclo-quaternionic lattices, J. Alg. 199 (1998), 472-498.
-
NOTES
CycloQuaternionic lattice of type Delta6
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe