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Properties

Label 3.284.568.9.1
Class number $9$
Dimension $3$
Determinant $284$
Level $568$

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Lattice Invariants

Dimension:$3$
Determinant:$284$
Level:$568$
Density:$0.0878788663418127500971481715865\dots$
Group order:$16$
Hermite number:$0.304268655646697039612331651130\dots$
Minimal vector length:$2$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 1 \\ 1 & 1 & 72 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$9$
 
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 1 \\ 1 & 1 & 72 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -2 \\ 0 & 8 & 1 \\ -2 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 0 \\ 0 & 8 & -3 \\ 0 & -3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 2 \\ 2 & 6 & -1 \\ 2 & -1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 4 & 0 \\ -1 & 0 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & -1 \\ 2 & 4 & 0 \\ -1 & 0 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 4 & -2 \\ -1 & -2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 4 & 0 \\ -1 & 0 & 36 \end{array}\right)$
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Comments

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