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Properties

Label 3.368.736.10.4
Class number $10$
Dimension $3$
Determinant $368$
Level $736$

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Lattice Invariants

Dimension:$3$
Determinant:$368$
Level:$736$
Density:$0.218355783789762129544751889458\dots$
Group order:$4$
Hermite number:$0.558184001999648116610071300049\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 2 q^{6} \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 2 q^{12} \) \(\mathstrut +\mathstrut 4 q^{16} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut 4 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 6 & 0 \\ 0 & 0 & 16 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$10$
 
$\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 6 & 0 \\ 0 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 12 & 0 \\ 0 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 8 & -1 \\ 0 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 16 & -7 \\ -1 & -7 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 10 & 5 \\ 1 & 5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 8 & 2 \\ -1 & 2 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 0 \\ -3 & 8 & -3 \\ 0 & -3 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & -1 \\ -1 & 8 & 0 \\ -1 & 0 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 10 & 2 \\ 1 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & 1 \\ -2 & 6 & 1 \\ 1 & 1 & 12 \end{array}\right)$
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Comments

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