Properties

Label 3.1766.3532.40.18
Class number $40$
Dimension $3$
Determinant $1766$
Level $3532$

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Lattice Invariants

Dimension:$3$
Determinant:$1766$
Level:$3532$
Density:$0.183117625538512957928344254472\dots$
Group order:$2$
Hermite number:$0.496387706553942704653205914321\dots$
Minimal vector length:$6$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{6} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 6 & 1 \\ 3 & 1 & 52 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$40$
 
$\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 6 & 1 \\ 3 & 1 & 52 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & -1 \\ 4 & 10 & -2 \\ -1 & -2 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 1 \\ 1 & 10 & 4 \\ 1 & 4 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 10 & 2 \\ 1 & 2 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -2 & -4 \\ -2 & 10 & 1 \\ -4 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -2 \\ -1 & 8 & 1 \\ -2 & 1 & 58 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 2 & 3 \\ 2 & 10 & -2 \\ 3 & -2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -5 & 1 \\ -5 & 14 & -3 \\ 1 & -3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 3 & 0 \\ 3 & 12 & -1 \\ 0 & -1 & 16 \end{array}\right)$ ...
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Comments

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