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Properties

Label 5.29282.44.1.1
Class number $1$
Dimension $5$
Determinant $29282$
Level $44$

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Lattice Invariants

Dimension:$5$
Determinant:$29282$
Level:$44$
Density:$0.0307608339378022238420167975148\dots$
Group order:$96$
Hermite number:$0.511375413959140060903243473938\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 12 q^{12} \) \(\mathstrut +\mathstrut 16 q^{14} \) \(\mathstrut +\mathstrut 18 q^{16} \) \(\mathstrut +\mathstrut 28 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrrrr} 4 & 1 & -2 & -2 & 2 \\ 1 & 14 & -6 & 5 & 6 \\ -2 & -6 & 12 & 1 & -1 \\ -2 & 5 & 1 & 12 & -1 \\ 2 & 6 & -1 & -1 & 12 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$1$
 
$\left(\begin{array}{rrrrr} 4 & -2 & -2 & 1 & 1 \\ -2 & 12 & 1 & -6 & 5 \\ -2 & 1 & 12 & 5 & -6 \\ 1 & -6 & 5 & 14 & -8 \\ 1 & 5 & -6 & -8 & 14 \end{array}\right)$
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