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Properties

Label 3.106.212.4.1
Class number $4$
Dimension $3$
Determinant $106$
Level $212$

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Lattice Invariants

Dimension:$3$
Determinant:$106$
Level:$212$
Density:$0.143843646198050812858328432621\dots$
Group order:$12$
Hermite number:$0.422598586964365107016310167805\dots$
Minimal vector length:$2$
Kissing number:$6$
Normalized minimal vectors: $(1, -1, 0)$, $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 6 q^{2} \) \(\mathstrut +\mathstrut 6 q^{6} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 12 q^{14} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 36 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$4$
 
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 4 & 1 \\ -1 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 6 & 2 \\ -1 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & -1 \\ 2 & 6 & -2 \\ -1 & -2 & 6 \end{array}\right)$
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Comments

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