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Properties

Label 3.752.1504.19.4
Class number $19$
Dimension $3$
Determinant $752$
Level $1504$

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Lattice Invariants

Dimension:$3$
Determinant:$752$
Level:$1504$
Density:$0.0540050901667175730318535394340\dots$
Group order:$8$
Hermite number:$0.219933160634218254154649078878\dots$
Minimal vector length:$2$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{2} \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 6 q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 16 & 0 \\ 1 & 0 & 24 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$19$
 
$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 16 & 0 \\ 1 & 0 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 16 & 8 \\ -1 & 8 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 12 & 0 \\ 0 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 0 & 3 \\ 0 & 8 & -3 \\ 3 & -3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & 0 \\ -1 & 8 & 0 \\ 0 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 8 & 3 \\ 1 & 3 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & -1 \\ 1 & 12 & -4 \\ -1 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 3 \\ -3 & 8 & -4 \\ 3 & -4 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 12 & -5 \\ -1 & -5 & 18 \end{array}\right)$ ...
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Comments

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