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Properties

Label 6.4.4.1.1
Class number $1$
Dimension $6$
Determinant $4$
Level $4$

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Lattice Invariants

Dimension:$6$
Determinant:$4$
Level:$4$
Density:$0.322982048753123126827878281948\dots$
Group order:$46080$
Hermite number:$1.58740105196819947475170563927\dots$
Minimal vector length:$2$
Kissing number:$60$
Normalized minimal vectors: $(1, -1, -2, -2, -2, -1)$, $(1, -1, -2, -2, -1, -1)$, $(1, -1, -2, -2, -1, 0)$, $(1, -1, -2, -1, -1, -1)$, $(1, -1, -2, -1, -1, 0)$, $(1, -1, -2, -1, 0, 0)$, $(1, -1, -1, -1, -1, -1)$, $(1, -1, -1, -1, -1, 0)$, $(1, -1, -1, -1, 0, 0)$, $(1, -1, -1, 0, 0, 0)$, $(1, 0, -1, -1, -1, -1)$, $(1, 0, -1, -1, -1, 0)$, $(1, 0, -1, -1, 0, 0)$, $(1, 0, -1, 0, 0, 0)$, $(1, 0, 0, 0, 0, 0)$, $(0, 1, 0, 0, 0, 0)$, $(0, 1, 1, 0, 0, 0)$, $(0, 1, 1, 1, 0, 0)$ ...
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 60 q^{2} \) \(\mathstrut +\mathstrut 252 q^{4} \) \(\mathstrut +\mathstrut 544 q^{6} \) \(\mathstrut +\mathstrut 1020 q^{8} \) \(\mathstrut +\mathstrut 1560 q^{10} \) \(\mathstrut +\mathstrut 2080 q^{12} \) \(\mathstrut +\mathstrut 3264 q^{14} \) \(\mathstrut +\mathstrut 4092 q^{16} \) \(\mathstrut +\mathstrut 4380 q^{18} \) \(\mathstrut +\mathstrut 6552 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

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