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Properties

Label 3.38.76.2.1
Class number $2$
Dimension $3$
Determinant $38$
Level $76$

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Lattice Invariants

Dimension:$3$
Determinant:$38$
Level:$76$
Density:$0.240243594715222648463532686124\dots$
Group order:$4$
Hermite number:$0.594888349259002887695722516016\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 4 q^{6} \) \(\mathstrut +\mathstrut 8 q^{8} \) \(\mathstrut +\mathstrut 10 q^{10} \) \(\mathstrut +\mathstrut 4 q^{12} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 12 q^{16} \) \(\mathstrut +\mathstrut 14 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 2 & 1 \\ 0 & 1 & 6 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$2$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 4 & 0 \\ 1 & 0 & 6 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 10 \end{array}\right)$
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Comments

This is the monoclinic C Bravais lattice of even holotype.