Lattice Invariants
Dimension: | $7$ |
Determinant: | $64$ |
Level: | $8$ |
Density: | $0.0522017821428245621779939869460\dots$ |
Group order: | $92160$ |
Hermite number: | $1.10408951367381233764950538762\dots$ |
Minimal vector length: | $2$ |
Kissing number: | $12$ |
Normalized minimal vectors: |
|
Download this list for gp, magma, sage |
Theta Series
Gram Matrix
$\left(\begin{array}{rrrrrrr} 2 & 0 & 0 & 1 & 0 & 0 & 0 \\ 0 & 2 & 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 2 & -1 & 0 & 0 & 0 \\ 1 & 1 & -1 & 4 & -1 & -1 & -1 \\ 0 & 0 & 0 & -1 & 2 & 0 & 0 \\ 0 & 0 & 0 & -1 & 0 & 2 & 0 \\ 0 & 0 & 0 & -1 & 0 & 0 & 2 \end{array}\right)$
Genus Structure
Class number: | $1$ |
$\left(\begin{array}{rrrrrrr} 2 & 0 & 0 & 0 & 0 & -1 & 1 \\ 0 & 2 & 0 & 0 & 0 & 1 & -1 \\ 0 & 0 & 2 & 0 & 0 & -1 & 1 \\ 0 & 0 & 0 & 2 & 0 & -1 & 1 \\ 0 & 0 & 0 & 0 & 2 & -1 & 1 \\ -1 & 1 & -1 & -1 & -1 & 4 & -3 \\ 1 & -1 & 1 & 1 & 1 & -3 & 4 \end{array}\right)$ | |
Download this matrix for gp, magma, sage |