Properties

 Label 3.752.1504.19.19 Class number 19 Dimension 3 Determinant 752 Level 1504

Lattice Invariants

Dimension:$3$
Determinant:$752$
Level:$1504$
Label:$3.752.1504.19.19$
Density:$0.603795263718929719393301632499\dots$
Group order:$4$
Hermite number:$1.09966580317109127077324539439\dots$
Minimal vector length:$10$
Kissing number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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Theta Series

$1$ $\mathstrut +\mathstrut 4q^{10}$ $\mathstrut +\mathstrut 6q^{12}$ $\mathstrut +\mathstrut 4q^{16}$ $\mathstrut +\mathstrut O(q^{21})$

Gram Matrix

$\left(\begin{array}{rrr} 10 & 2 & 5 \\ 2 & 10 & 5 \\ 5 & 5 & 12 \end{array}\right)$

Genus Structure

 Class number: $19$ Genus representatives: $\left(\begin{array}{rrr} 10 & 2 & 5 \\ 2 & 10 & 5 \\ 5 & 5 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -1 & -1 \\ -1 & 10 & 2 \\ -1 & 2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 0 & 1 \\ 0 & 8 & 1 \\ 1 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & 1 \\ 3 & 10 & -3 \\ 1 & -3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & -4 \\ 3 & 8 & -3 \\ -4 & -3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -1 \\ -1 & 16 & 8 \\ -1 & 8 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 14 & 3 \\ -1 & 3 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & 1 \\ 2 & 6 & -1 \\ 1 & -1 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 12 & 5 \\ -1 & 5 & 18 \end{array}\right)$ ... Download the complete list for gp, magma, sage