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Properties

Label 3.694.1388.20.19
Class number $20$
Dimension $3$
Determinant $694$
Level $1388$

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Lattice Invariants

Dimension:$3$
Determinant:$694$
Level:$1388$
Density:$0.449732080085887832751285926422\dots$
Group order:$2$
Hermite number:$0.903587394174438707172503021056\dots$
Minimal vector length:$8$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 8 & 3 & 3 \\ 3 & 10 & -2 \\ 3 & -2 & 12 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$20$
 
$\left(\begin{array}{rrr} 8 & 3 & 3 \\ 3 & 10 & -2 \\ 3 & -2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 10 & 2 \\ -1 & 2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 1 \\ -1 & 10 & -1 \\ 1 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 3 \\ 4 & 10 & 2 \\ 3 & 2 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 58 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 14 & -2 \\ 0 & -2 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 10 & 4 \\ 1 & 4 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 8 & 3 \\ -1 & 3 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 16 & -5 \\ 0 & -5 & 24 \end{array}\right)$ ...
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Comments

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