Properties

Label 3.752.1504.19.1
Class number 19
Dimension 3
Determinant 752
Level 1504

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Lattice Invariants

Dimension:$3$
Determinant:$752$
Level:$1504$
Label:$3.752.1504.19.1$
Density:$0.0540050901667175730318535394340\dots$
Group order:$4$
Hermite number:$0.219933160634218254154649078878\dots$
Minimal vector length:$2$
Kissing Number:$2$
Normalized minimal vectors: $(1, 0, 0)$
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Theta Series

\(1 \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 4q^{4} \) \(\mathstrut +\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut +\mathstrut 2q^{18} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 108 \end{array}\right)$

Genus Structure

Class number:$19$
 
Genus representatives: $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 4 & 1 \\ 1 & 1 & 108 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 12 & 1 \\ -1 & 1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 16 & -8 \\ 1 & -8 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 12 & 5 \\ -1 & 5 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & -4 \\ 3 & 8 & -3 \\ -4 & -3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & -1 \\ -2 & 8 & -2 \\ -1 & -2 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & 1 \\ -2 & 6 & 1 \\ 1 & 1 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -1 & -1 \\ -1 & 10 & 2 \\ -1 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 14 & -3 \\ -1 & -3 & 28 \end{array}\right)$ ...
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Comments

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