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Properties

Label 3.718.1436.25.21
Class number $25$
Dimension $3$
Determinant $718$
Level $1436$

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Lattice Invariants

Dimension:$3$
Determinant:$718$
Level:$1436$
Density:$0.156324262039227978377949548311\dots$
Group order:$2$
Hermite number:$0.446702630502489123225475530185\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 2 q^{12} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 12 & 5 \\ 2 & 5 & 18 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$25$
 
$\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 12 & 5 \\ 2 & 5 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & -2 \\ -1 & 8 & 1 \\ -2 & 1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 18 & 8 \\ -1 & 8 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 14 & -3 \\ -1 & -3 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & -5 \\ 0 & -5 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & -3 \\ 0 & -3 & 46 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & -2 \\ 3 & 8 & 1 \\ -2 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & -1 \\ 0 & -1 & 180 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 16 & -7 \\ 1 & -7 & 26 \end{array}\right)$ ...
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Comments

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