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Properties

Label 3.156.312.4.2
Class number $4$
Dimension $3$
Determinant $156$
Level $312$

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Lattice Invariants

Dimension:$3$
Determinant:$156$
Level:$312$
Density:$0.335371621084638823318377746428\dots$
Group order:$4$
Hermite number:$0.743050718639374356134245382070\dots$
Minimal vector length:$4$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 2 q^{6} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 6 q^{12} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 8 q^{16} \) \(\mathstrut +\mathstrut 4 q^{18} \) \(\mathstrut +\mathstrut 8 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 4 & 2 \\ 2 & 2 & 12 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$4$
 
$\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 4 & 2 \\ 2 & 2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 0 \\ -2 & 6 & -1 \\ 0 & -1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 0 \\ 0 & 6 & 3 \\ 0 & 3 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 4 & 0 \\ -1 & 0 & 20 \end{array}\right)$
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Comments

This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.