Lattice Invariants
Dimension: | $3$ |
Determinant: | $334$ |
Level: | $668$ |
Density: | $0.0810345794168783541287379467716\dots$ |
Group order: | $4$ |
Hermite number: | $0.288257870120516896973848491294\dots$ |
Minimal vector length: | $2$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
|
Download this vector for gp, magma, sage |
Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 14 & 7 \\ 1 & 7 & 16 \end{array}\right)$
Genus Structure
Class number: | $13$ |
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 14 & 7 \\ 1 & 7 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 2 & 1 \\ -1 & 1 & 112 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & 5 \\ 0 & 5 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 6 & 3 \\ 1 & 3 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & -1 \\ 0 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 2 & 0 \\ -1 & 0 & 84 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & -1 \\ 0 & -1 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 8 & 3 \\ 0 & 3 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 8 & -3 \\ 1 & -3 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 10 & -2 \\ 0 & -2 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -1 & -2 \\ -1 & 8 & -1 \\ -2 & -1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & -1 & 42 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & 1 \\ 0 & 1 & 28 \end{array}\right)$ | |
Download this list for gp, magma, sage |
Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.