Lattice Invariants
Dimension: | $3$ |
Determinant: | $362$ |
Level: | $724$ |
Density: | $0.220157925359634977331772054027\dots$ |
Group order: | $2$ |
Hermite number: | $0.561251008625324216181764918465\dots$ |
Minimal vector length: | $4$ |
Kissing number: | $2$ |
Normalized minimal vectors: |
|
Download this vector for gp, magma, sage |
Theta Series
Gram Matrix
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 6 & 0 \\ 1 & 0 & 16 \end{array}\right)$
Genus Structure
Class number: | $10$ |
$\left(\begin{array}{rrr} 4 & 1 & 1 \\ 1 & 6 & 0 \\ 1 & 0 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 1 \\ -1 & 12 & 4 \\ 1 & 4 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -1 \\ 1 & 8 & -1 \\ -1 & -1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 4 & -1 \\ 0 & -1 & 52 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 14 & -6 \\ -1 & -6 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & 1 & 3 \\ 1 & 8 & -2 \\ 3 & -2 & 10 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 4 & -1 \\ -1 & -1 & 46 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 10 & -3 \\ 0 & -3 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & -1 \\ 0 & 6 & 2 \\ -1 & 2 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 6 & -2 & 1 \\ -2 & 6 & -2 \\ 1 & -2 & 12 \end{array}\right)$ | |
Download this list for gp, magma, sage |
Comments
This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.