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Properties

Label 3.1658.3316.40.13
Class number $40$
Dimension $3$
Determinant $1658$
Level $3316$

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Lattice Invariants

Dimension:$3$
Determinant:$1658$
Level:$3316$
Density:$0.102871801711073954965061860328\dots$
Group order:$2$
Hermite number:$0.337959881573982579615545996882\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 8 & 2 \\ 0 & 2 & 54 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$40$
 
$\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 8 & 2 \\ 0 & 2 & 54 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 6 & 2 \\ -1 & 2 & 70 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 0 & 1 \\ 0 & 12 & 1 \\ 1 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 2 & -1 \\ 2 & 10 & -1 \\ -1 & -1 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 18 & -7 \\ 1 & -7 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -1 & 2 \\ -1 & 10 & 2 \\ 2 & 2 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -3 & -5 \\ -3 & 12 & -1 \\ -5 & -1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 0 & 1 \\ 0 & 12 & 5 \\ 1 & 5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 22 & -8 \\ 1 & -8 & 22 \end{array}\right)$ ...
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Comments

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