Properties

Label 3.614.1228.16.2
Class number $16$
Dimension $3$
Determinant $614$
Level $1228$

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Lattice Invariants

Dimension:$3$
Determinant:$614$
Level:$1228$
Density:$0.0597667210798695915945394384638\dots$
Group order:$4$
Hermite number:$0.235310083862595860087820501968\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 8 q^{16} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 1 \\ 0 & 1 & 88 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$16$
 
$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 1 \\ 0 & 1 & 88 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 10 & 2 \\ -1 & 2 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 10 & 0 \\ -1 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -4 & 1 \\ -4 & 10 & -2 \\ 1 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 10 & 3 \\ 1 & 3 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 6 & -1 \\ 1 & -1 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 10 & -3 \\ 2 & -3 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & -1 \\ 0 & 10 & 4 \\ -1 & 4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & -2 \\ -3 & 10 & -2 \\ -2 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 6 & -1 \\ 0 & -1 & 56 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 4 & -2 \\ -1 & -2 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 154 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & -4 \\ 0 & -4 & 34 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & -3 \\ -2 & 8 & 3 \\ -3 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 14 & -1 \\ 0 & -1 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 8 & -3 \\ -1 & -3 & 40 \end{array}\right)$
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Comments

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