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Properties

Label 3.190.380.6.6
Class number $6$
Dimension $3$
Determinant $190$
Level $380$

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Lattice Invariants

Dimension:$3$
Determinant:$190$
Level:$380$
Density:$0.558275664819036904968825533739\dots$
Group order:$4$
Hermite number:$1.04367845129369708528286365411\dots$
Minimal vector length:$6$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 4 q^{6} \) \(\mathstrut +\mathstrut 6 q^{8} \) \(\mathstrut +\mathstrut 4 q^{10} \) \(\mathstrut +\mathstrut 2 q^{14} \) \(\mathstrut +\mathstrut 4 q^{18} \) \(\mathstrut +\mathstrut 8 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

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

Genus Structure

Genus representatives:
Class number:$6$
 
$\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 6 & 3 \\ 3 & 3 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & -1 \\ 0 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 10 & -5 \\ 0 & -5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & 0 \\ -1 & 0 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & 0 \\ 0 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 6 & -2 \\ 0 & -2 & 18 \end{array}\right)$
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Comments

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