Properties

Label 3.568.1136.16.6
Class number $16$
Dimension $3$
Determinant $568$
Level $1136$

Downloads

Learn more

Lattice Invariants

Dimension:$3$
Determinant:$568$
Level:$1136$
Density:$0.175757732683625500194296343173\dots$
Group order:$4$
Hermite number:$0.482996384054516717939743563457\dots$
Minimal vector length:$4$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$
Download this vector for gp, magma, sage

Theta Series

\(1 \) \(\mathstrut +\mathstrut 2 q^{4} \) \(\mathstrut +\mathstrut 2 q^{8} \) \(\mathstrut +\mathstrut 4 q^{12} \) \(\mathstrut +\mathstrut 2 q^{16} \) \(\mathstrut +\mathstrut 2 q^{18} \) \(\mathstrut +\mathstrut 2 q^{20} \) \(\mathstrut +\mathstrut O(q^{21}) \)

Gram Matrix

$\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 8 & 0 \\ 1 & 0 & 18 \end{array}\right)$

Genus Structure

Genus representatives:
Class number:$16$
 
$\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 8 & 0 \\ 1 & 0 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 8 & 4 \\ -1 & 4 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 8 & 0 \\ 1 & 0 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 0 & -3 \\ 0 & 8 & 0 \\ -3 & 0 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 4 & 1 \\ -1 & 1 & 36 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 0 & -3 \\ 0 & 8 & -4 \\ -3 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 8 & -1 \\ 0 & -1 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 8 & 0 \\ 1 & 0 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 8 & -4 \\ 1 & -4 & 40 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & 1 \\ -2 & 8 & -2 \\ 1 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 2 & -3 \\ 2 & 6 & -3 \\ -3 & -3 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -2 & -3 \\ -2 & 8 & 4 \\ -3 & 4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 3 \\ 4 & 8 & -1 \\ 3 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 0 \\ 4 & 8 & 1 \\ 0 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 6 & 1 \\ 1 & 1 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 4 & 0 \\ 4 & 10 & -5 \\ 0 & -5 & 12 \end{array}\right)$
Download this list for gp, magma, sage

Comments

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