Properties

Label 3.446.892.13.4
Class number $13$
Dimension $3$
Determinant $446$
Level $892$

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Lattice Invariants

Dimension:$3$
Determinant:$446$
Level:$892$
Density:$0.0701255348166987686198554233288\dots$
Group order:$4$
Hermite number:$0.261769097745826690902456187389\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 4 q^{16} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & 1 \\ 0 & 1 & 28 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$13$
 
$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & 1 \\ 0 & 1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 10 & -5 \\ -1 & -5 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -1 \\ -1 & 8 & -3 \\ -1 & -3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 10 & 2 \\ 1 & 2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 4 & -1 \\ 0 & -1 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 14 & -1 \\ 0 & -1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & -1 \\ 0 & -1 & 64 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 10 & 0 \\ 1 & 0 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 0 \\ -1 & 8 & -2 \\ 0 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & -1 & 56 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 1 \\ -2 & 10 & -4 \\ 1 & -4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 16 & 5 \\ 0 & 5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & 0 \\ -1 & 0 & 112 \end{array}\right)$
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Comments

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