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Properties

Label 3.1942.3884.56.2
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:$12$
Hermite number:$0.160304945380893321759978963848\dots$
Minimal vector length:$2$
Kissing number:$6$
Normalized minimal vectors: $(1, -1, 0)$, $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 6 q^{6} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 12 q^{14} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 648 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$56$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 648 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 14 & 1 \\ 0 & 1 & 72 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 8 & 1 \\ -1 & 1 & 122 \end{array}\right)$, $\left(\begin{array}{rrr} 12 & -3 & 5 \\ -3 & 14 & -6 \\ 5 & -6 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & 0 \\ 3 & 16 & -5 \\ 0 & -5 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 18 & 0 \\ -1 & 0 & 56 \end{array}\right)$, $\left(\begin{array}{rrr} 12 & -3 & -1 \\ -3 & 14 & 5 \\ -1 & 5 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 30 & -13 \\ 0 & -13 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & -3 \\ -1 & 18 & 3 \\ -3 & 3 & 20 \end{array}\right)$ ...
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Comments

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