Properties

 Label 3.752.1504.19.12 Class number 19 Dimension 3 Determinant 752 Level 1504

Lattice Invariants

Dimension:$3$
Determinant:$752$
Level:$1504$
Label:$3.752.1504.19.12$
Density:$0.280618680108279619324954075667\dots$
Group order:$4$
Hermite number:$0.659799481902654762463947236634\dots$
Minimal vector length:$6$
Kissing Number:$2$
Normalized minimal vectors: $(1, 0, 0)$

Theta Series

$1$ $\mathstrut +\mathstrut 2q^{6}$ $\mathstrut +\mathstrut 2q^{8}$ $\mathstrut +\mathstrut 2q^{12}$ $\mathstrut +\mathstrut 4q^{16}$ $\mathstrut +\mathstrut O(q^{21})$

Gram Matrix

$\left(\begin{array}{rrr} 6 & 1 & 0 \\ 1 & 8 & 0 \\ 0 & 0 & 16 \end{array}\right)$

Genus Structure

 Class number: $19$ Genus representatives: $\left(\begin{array}{rrr} 6 & 1 & 0 \\ 1 & 8 & 0 \\ 0 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & 0 \\ 1 & 12 & 0 \\ 0 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 3 & 3 \\ 3 & 8 & 4 \\ 3 & 4 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 16 & 0 \\ -1 & 0 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 2 & 1 \\ 2 & 8 & 3 \\ 1 & 3 & 28 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 12 & 1 \\ 1 & 1 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -1 & 1 \\ -1 & 10 & -2 \\ 1 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 8 & 2 \\ -1 & 2 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 16 & 8 \\ -1 & 8 & 28 \end{array}\right)$ ... Download the complete list for gp, magma, sage