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Properties

Label 4.13.13.1.1
Class number $1$
Dimension $4$
Determinant $13$
Level $13$

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Lattice Invariants

Dimension:$4$
Determinant:$13$
Level:$13$
Density:$0.342166968621853260831718699231\dots$
Group order:$48$
Hermite number:$1.05328077569585321091257541266\dots$
Minimal vector length:$2$
Kissing number:$12$
Normalized minimal vectors: $(1, -1, -1, 0)$, $(1, -1, 0, 0)$, $(1, 0, -1, 0)$, $(1, 0, 0, 0)$, $(0, 1, 0, 0)$, $(0, 0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 12 q^{2} \) \(\mathstrut +\mathstrut 14 q^{4} \) \(\mathstrut +\mathstrut 48 q^{6} \) \(\mathstrut +\mathstrut 36 q^{8} \) \(\mathstrut +\mathstrut 56 q^{10} \) \(\mathstrut +\mathstrut 56 q^{12} \) \(\mathstrut +\mathstrut 84 q^{14} \) \(\mathstrut +\mathstrut 70 q^{16} \) \(\mathstrut +\mathstrut 156 q^{18} \) \(\mathstrut +\mathstrut 48 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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