Properties

Label 3.278.556.9.9
Class number $9$
Dimension $3$
Determinant $278$
Level $556$

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Lattice Invariants

Dimension:$3$
Determinant:$278$
Level:$556$
Density:$0.461533362421209896937330652325\dots$
Group order:$2$
Hermite number:$0.919326230556052080739597185138\dots$
Minimal vector length:$6$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{6} \) \(\mathstrut +\mathstrut 4 q^{8} \) \(\mathstrut +\mathstrut 6 q^{10} \) \(\mathstrut +\mathstrut 2 q^{12} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 8 & -3 \\ 1 & -3 & 8 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$9$
 
$\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 8 & -3 \\ 1 & -3 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & -1 \\ 0 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 6 & -1 \\ 1 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -2 \\ 1 & 8 & -1 \\ -2 & -1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 10 & 4 \\ -1 & 4 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 8 & -1 \\ -1 & -1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & -1 \\ 0 & -1 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 6 & 2 \\ 0 & 2 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 70 \end{array}\right)$
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Comments

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