Properties

Label 3.652.1304.14.1
Class number $14$
Dimension $3$
Determinant $652$
Level $1304$

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Lattice Invariants

Dimension:$3$
Determinant:$652$
Level:$1304$
Density:$0.0579989081564289999105172051831\dots$
Group order:$16$
Hermite number:$0.230646816028513698781501223695\dots$
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

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 1 \\ 1 & 1 & 164 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$14$
 
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 1 \\ 1 & 1 & 164 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 18 & -5 \\ 1 & -5 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 20 & -8 \\ 0 & -8 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & 3 \\ -2 & 8 & -1 \\ 3 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 12 & 5 \\ 0 & 5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & -2 \\ 0 & -2 & 44 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 3 \\ -3 & 10 & -5 \\ 3 & -5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 0 \\ 1 & 8 & -1 \\ 0 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 12 & -2 \\ -1 & -2 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 8 & 1 \\ 1 & 1 & 44 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & 0 \\ 3 & 8 & 1 \\ 0 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & 1 \\ -2 & 10 & 1 \\ 1 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -3 & 2 \\ -3 & 8 & 1 \\ 2 & 1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 4 & -2 \\ -1 & -2 & 42 \end{array}\right)$
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Comments

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