Properties

Label 3.206.412.7.6
Class number $7$
Dimension $3$
Determinant $206$
Level $412$

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Lattice Invariants

Dimension:$3$
Determinant:$206$
Level:$412$
Density:$0.291846842561602460468250623998\dots$
Group order:$2$
Hermite number:$0.677284158782578041416617781550\dots$
Minimal vector length:$4$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{4} \) \(\mathstrut +\mathstrut 2 q^{6} \) \(\mathstrut +\mathstrut 2 q^{10} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 10 q^{16} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 4 & 0 \\ 1 & 0 & 14 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$7$
 
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 4 & 0 \\ 1 & 0 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & -3 \\ 0 & -3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & -1 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 4 & 0 \\ -1 & 0 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 10 & 3 \\ -1 & 3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 2 \\ 1 & 6 & 1 \\ 2 & 1 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 2 & 1 \\ 0 & 1 & 52 \end{array}\right)$
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Comments

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