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Properties

Label 3.1942.3884.56.33
Class number $56$
Dimension $3$
Determinant $1942$
Level $3884$

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Lattice Invariants

Dimension:$3$
Determinant:$1942$
Level:$3884$
Density:$0.0950525990754387231066609878264\dots$
Group order:$2$
Hermite number:$0.320609890761786643519957927697\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 4 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 18 & 5 \\ 1 & 5 & 30 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$56$
 
$\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 18 & 5 \\ 1 & 5 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 32 & 10 \\ 0 & 10 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 30 & 7 \\ 0 & 7 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & 0 \\ 3 & 16 & -5 \\ 0 & -5 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 22 & -9 \\ 1 & -9 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 4 & 0 \\ -1 & 0 & 278 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 10 & -4 \\ -1 & -4 & 104 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 30 & -13 \\ 0 & -13 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 14 & -3 \\ 0 & -3 & 70 \end{array}\right)$ ...
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Comments

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