Properties

Label 3.334.668.13.11
Class number $13$
Dimension $3$
Determinant $334$
Level $668$

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Lattice Invariants

Dimension:$3$
Determinant:$334$
Level:$668$
Density:$0.0810345794168783541287379467716\dots$
Group order:$4$
Hermite number:$0.288257870120516896973848491294\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 14 & 7 \\ 1 & 7 & 16 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$13$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 14 & 7 \\ 1 & 7 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 2 & 1 \\ -1 & 1 & 112 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & 5 \\ 0 & 5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 6 & 3 \\ 1 & 3 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & -1 \\ 0 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & 0 \\ -1 & 0 & 84 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & -1 \\ 0 & -1 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & 3 \\ 0 & 3 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 8 & -3 \\ 1 & -3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & -2 \\ 0 & -2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & -2 \\ -1 & 8 & -1 \\ -2 & -1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & -1 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 28 \end{array}\right)$
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Comments

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