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Properties

Label 5.6.12.1.2
Class number $1$
Dimension $5$
Determinant $6$
Level $12$

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Lattice Invariants

Dimension:$5$
Determinant:$6$
Level:$12$
Density:$0.0671541520716558210194418957864\dots$
Group order:$192$
Hermite number:$0.698827118771579245232977102772\dots$
Minimal vector length:$1$
Kissing number:$6$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0)$, $(0, 0, 1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q \) \(\mathstrut +\mathstrut 14 q^{2} \) \(\mathstrut +\mathstrut 22 q^{3} \) \(\mathstrut +\mathstrut 42 q^{4} \) \(\mathstrut +\mathstrut 68 q^{5} \) \(\mathstrut +\mathstrut 76 q^{6} \) \(\mathstrut +\mathstrut 108 q^{7} \) \(\mathstrut +\mathstrut 142 q^{8} \) \(\mathstrut +\mathstrut 114 q^{9} \) \(\mathstrut +\mathstrut 168 q^{10} \) \(\mathstrut +\mathstrut 224 q^{11} \) \(\mathstrut +\mathstrut 154 q^{12} \) \(\mathstrut +\mathstrut 276 q^{13} \) \(\mathstrut +\mathstrut 340 q^{14} \) \(\mathstrut +\mathstrut 224 q^{15} \) \(\mathstrut +\mathstrut 426 q^{16} \) \(\mathstrut +\mathstrut 412 q^{17} \) \(\mathstrut +\mathstrut 266 q^{18} \) \(\mathstrut +\mathstrut 528 q^{19} \) \(\mathstrut +\mathstrut 476 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 0 & 3 \end{array}\right)$
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