Properties

Label 3.658.1316.14.14
Class number $14$
Dimension $3$
Determinant $658$
Level $1316$

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Lattice Invariants

Dimension:$3$
Determinant:$658$
Level:$1316$
Density:$0.461870958961580692166477466041\dots$
Group order:$2$
Hermite number:$0.919774480608222031091510272398\dots$
Minimal vector length:$8$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 8 & 3 & 4 \\ 3 & 8 & 2 \\ 4 & 2 & 14 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$14$
 
$\left(\begin{array}{rrr} 8 & 3 & 4 \\ 3 & 8 & 2 \\ 4 & 2 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 4 \\ 1 & 8 & 4 \\ 4 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 0 \\ 1 & 8 & 0 \\ 0 & 0 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 6 & -2 \\ -1 & -2 & 56 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & -1 \\ 0 & 8 & 1 \\ -1 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & 0 \\ 0 & 0 & 94 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & -2 \\ 2 & 12 & -5 \\ -2 & -5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 12 & 0 \\ 0 & 0 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 14 & 7 \\ 1 & 7 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 12 & 1 \\ -1 & 1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 2 \\ -1 & 10 & 1 \\ 2 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 12 & -5 \\ -1 & -5 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 14 & 0 \\ -1 & 0 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 2 & 1 \\ -1 & 1 & 220 \end{array}\right)$
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Comments

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