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Properties

Label 5.24.48.1.1
Class number $1$
Dimension $5$
Determinant $24$
Level $48$

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Lattice Invariants

Dimension:$5$
Determinant:$24$
Level:$48$
Density:$0.189940625258801879052699698349\dots$
Group order:$144$
Hermite number:$1.05922384104881225329467473346\dots$
Minimal vector length:$2$
Kissing number:$12$
Normalized minimal vectors: $(1, -1, 0, 0, 0)$, $(1, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0)$, $(0, 0, 1, -1, 0)$, $(0, 0, 1, 0, 0)$, $(0, 0, 0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 12 q^{2} \) \(\mathstrut +\mathstrut 54 q^{4} \) \(\mathstrut +\mathstrut 48 q^{6} \) \(\mathstrut +\mathstrut 174 q^{8} \) \(\mathstrut +\mathstrut 144 q^{10} \) \(\mathstrut +\mathstrut 198 q^{12} \) \(\mathstrut +\mathstrut 240 q^{14} \) \(\mathstrut +\mathstrut 522 q^{16} \) \(\mathstrut +\mathstrut 228 q^{18} \) \(\mathstrut +\mathstrut 612 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 2 & 1 & 0 & 0 & -1 \\ 1 & 2 & 0 & 0 & -1 \\ 0 & 0 & 2 & 1 & -1 \\ 0 & 0 & 1 & 2 & 0 \\ -1 & -1 & -1 & 0 & 4 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 2 & 1 & 0 & 0 & -1 \\ 1 & 2 & 0 & 0 & -1 \\ 0 & 0 & 2 & 1 & -1 \\ 0 & 0 & 1 & 2 & 0 \\ -1 & -1 & -1 & 0 & 4 \end{array}\right)$
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