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Properties

Label 3.1942.3884.56.1
Class number $56$
Dimension $3$
Determinant $1942$
Level $3884$

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Lattice Invariants

Dimension:$3$
Determinant:$1942$
Level:$3884$
Density:$0.0336061686878244393520452261061\dots$
Group order:$8$
Hermite number:$0.160304945380893321759978963848\dots$
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

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 486 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$56$
 
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 486 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 18 & 1 \\ 0 & 1 & 54 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 18 & 8 \\ 1 & 8 & 58 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 162 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & -2 \\ 3 & 18 & -8 \\ -2 & -8 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 24 & -11 \\ 1 & -11 & 46 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & -3 \\ -3 & 16 & 4 \\ -3 & 4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & -3 \\ -2 & 14 & 7 \\ -3 & 7 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & -2 \\ 0 & -2 & 130 \end{array}\right)$ ...
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Comments

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