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Properties

Label 3.1090.2180.19.13
Class number $19$
Dimension $3$
Determinant $1090$
Level $2180$

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Lattice Invariants

Dimension:$3$
Determinant:$1090$
Level:$2180$
Density:$0.233083885373217872622878860285\dots$
Group order:$2$
Hermite number:$0.583009660459202363120902167865\dots$
Minimal vector length:$6$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

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

Gram Matrix

$\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 10 & 1 \\ 3 & 1 & 20 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$19$
 
$\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 10 & 1 \\ 3 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 20 & 6 \\ -1 & 6 & 30 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & -5 & -5 \\ -5 & 12 & 3 \\ -5 & 3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 1 \\ 1 & 10 & 1 \\ 1 & 1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 20 & -1 \\ 0 & -1 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 10 & 4 \\ -1 & 4 & 60 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -1 & -4 \\ -1 & 12 & 3 \\ -4 & 3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 4 \\ 1 & 14 & 6 \\ 4 & 6 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 3 & -2 \\ 3 & 8 & 2 \\ -2 & 2 & 30 \end{array}\right)$ ...
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Comments

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