Properties

Label 3.634.1268.16.9
Class number $16$
Dimension $3$
Determinant $634$
Level $1268$

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Lattice Invariants

Dimension:$3$
Determinant:$634$
Level:$1268$
Density:$0.305619364937532105607099453465\dots$
Group order:$2$
Hermite number:$0.698427768148489326467532706853\dots$
Minimal vector length:$6$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 6 & 2 \\ 3 & 2 & 20 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$16$
 
$\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 6 & 2 \\ 3 & 2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -1 \\ -1 & 12 & 2 \\ -1 & 2 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & -2 \\ -2 & 10 & 1 \\ -2 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 0 \\ 1 & 8 & 2 \\ 0 & 2 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 14 & 0 \\ -1 & 0 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & -2 \\ 0 & 8 & -1 \\ -2 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & -2 \\ 2 & 10 & -5 \\ -2 & -5 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & -1 \\ 2 & 12 & 5 \\ -1 & 5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 6 & 2 \\ 1 & 2 & 54 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & -1 \\ -2 & 6 & 0 \\ -1 & 0 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 2 & 1 \\ -1 & 1 & 212 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 4 & 1 \\ 1 & 1 & 80 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & 2 \\ 3 & 10 & 3 \\ 2 & 3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & -1 \\ -2 & 14 & 5 \\ -1 & 5 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 6 & 1 \\ 1 & 1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 10 & 5 \\ 1 & 5 & 36 \end{array}\right)$
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Comments

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