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Properties

Label 5.20736.24.1.2
Class number $1$
Dimension $5$
Determinant $20736$
Level $24$

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Lattice Invariants

Dimension:$5$
Determinant:$20736$
Level:$24$
Density:$0.0638573679162815547174301193362\dots$
Group order:$24$
Hermite number:$0.684896595632177400961874140096\dots$
Minimal vector length:$5$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{5} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 6 q^{9} \) \(\mathstrut +\mathstrut 6 q^{12} \) \(\mathstrut +\mathstrut 36 q^{17} \) \(\mathstrut +\mathstrut 36 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 5 & 2 & -2 & 2 & -1 \\ 2 & 8 & -2 & 2 & -4 \\ -2 & -2 & 8 & -2 & -2 \\ 2 & 2 & -2 & 8 & -4 \\ -1 & -4 & -2 & -4 & 17 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 5 & 2 & -2 & 2 & -1 \\ 2 & 8 & -2 & 2 & -4 \\ -2 & -2 & 8 & -2 & -2 \\ 2 & 2 & -2 & 8 & -4 \\ -1 & -4 & -2 & -4 & 17 \end{array}\right)$
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