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Properties

Label 3.1942.3884.56.48
Class number $56$
Dimension $3$
Determinant $1942$
Level $3884$

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Lattice Invariants

Dimension:$3$
Determinant:$1942$
Level:$3884$
Density:$0.268849349502595514816361808849\dots$
Group order:$2$
Hermite number:$0.641219781523573287039915855393\dots$
Minimal vector length:$8$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 8 & 3 & 1 \\ 3 & 14 & 4 \\ 1 & 4 & 20 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$56$
 
$\left(\begin{array}{rrr} 8 & 3 & 1 \\ 3 & 14 & 4 \\ 1 & 4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 1 \\ -3 & 18 & -10 \\ 1 & -10 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -3 & 3 \\ -3 & 14 & 1 \\ 3 & 1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & -1 \\ 1 & 12 & 4 \\ -1 & 4 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & 1 \\ -2 & 10 & -2 \\ 1 & -2 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 8 & -2 \\ 0 & -2 & 130 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 18 & -1 \\ 0 & -1 & 54 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & -2 \\ 1 & 14 & 0 \\ -2 & 0 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 20 & -2 \\ 0 & -2 & 50 \end{array}\right)$ ...
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Comments

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