Properties

Label 3.562.1124.17.16
Class number $17$
Dimension $3$
Determinant $562$
Level $1124$

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Lattice Invariants

Dimension:$3$
Determinant:$562$
Level:$1124$
Density:$0.499764547832232783716821582084\dots$
Group order:$2$
Hermite number:$0.969418303045297190715668766661\dots$
Minimal vector length:$8$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 2 q^{12} \) \(\mathstrut +\mathstrut 4 q^{14} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 8 & 3 & 3 \\ 3 & 8 & -1 \\ 3 & -1 & 12 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$17$
 
$\left(\begin{array}{rrr} 8 & 3 & 3 \\ 3 & 8 & -1 \\ 3 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 2 & -3 \\ 2 & 10 & 3 \\ -3 & 3 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 6 & 2 \\ -1 & 2 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 6 & 3 \\ 1 & 3 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & -1 \\ -1 & 8 & 4 \\ -1 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 8 & -1 \\ 1 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -2 \\ 1 & 12 & -4 \\ -2 & -4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 6 & 1 \\ -1 & 1 & 52 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 12 & -4 \\ 1 & -4 & 26 \end{array}\right)$ ...
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Comments

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