Properties

Label 3.1942.3884.56.38
Class number $56$
Dimension $3$
Determinant $1942$
Level $3884$

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Lattice Invariants

Dimension:$3$
Determinant:$1942$
Level:$3884$
Density:$0.174622774845126712628966612466\dots$
Group order:$2$
Hermite number:$0.480914836142679965279936891545\dots$
Minimal vector length:$6$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{6} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 16 & -3 \\ 1 & -3 & 22 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$56$
 
$\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 16 & -3 \\ 1 & -3 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 26 & -11 \\ 0 & -11 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -3 & 3 \\ -3 & 14 & 1 \\ 3 & 1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 1 \\ 4 & 10 & -3 \\ 1 & -3 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 30 & 13 \\ 0 & 13 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & -3 \\ 0 & -3 & 98 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 20 & -2 \\ 0 & -2 & 50 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 3 \\ 1 & 8 & 1 \\ 3 & 1 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & -1 \\ 3 & 14 & -4 \\ -1 & -4 & 20 \end{array}\right)$ ...
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Comments

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