Integral lattice 8.256.8.1.2

• Label: 8.256.8.1.2
• Class number: $1$
• Dimension: $8$
• Determinant: $256$
• Level: $8$

Lattice Invariants

Dimension:

$8$

Determinant:

$256$

Level:

$8$

Density:

$0.0802626177343159730646938776427\dots$

Group order:

$5806080$

Hermite number:

$1.50000000000000000000000000000\dots$

Minimal vector length:

$3$

Kissing number:

$56$

Normalized minimal vectors:

$(1, 0, -2, -1, -1, -1, 1, 0)$, $(1, 0, -1, -1, -1, 0, 1, 0)$, $(1, 0, -1, 0, -1, -1, 1, 0)$, $(1, 0, -1, 0, -1, 0, 0, 0)$, $(1, 0, -1, 0, 0, 0, 1, 0)$, $(1, 0, 0, 0, 0, 0, 0, 0)$, $(1, 1, -1, 0, -1, 0, 1, 0)$, $(1, 1, 0, 0, -1, 0, 0, 0)$, $(1, 1, 0, 0, 0, 0, 1, 0)$, $(1, 1, 0, 0, 0, 1, 0, 0)$, $(1, 1, 0, 1, 0, 0, 0, 0)$, $(1, 1, 1, 1, 0, 1, 0, 0)$, $(0, 1, 0, 0, 0, 0, 0, 0)$ ...

Download the complete list for gp, magma, sage

Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrrr} 3 & -1 & 1 & -1 & 1 & -1 & -1 & 0 \\ -1 & 3 & -1 & -1 & 1 & -1 & -1 & 0 \\ 1 & -1 & 3 & -1 & -1 & -1 & 1 & 0 \\ -1 & -1 & -1 & 3 & -1 & 1 & 1 & 0 \\ 1 & 1 & -1 & -1 & 3 & -1 & -1 & 0 \\ -1 & -1 & -1 & 1 & -1 & 3 & 1 & 0 \\ -1 & -1 & 1 & 1 & -1 & 1 & 3 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 4 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrrr} 3 & 1 & 1 & -1 & -1 & 1 & -1 & 0 \\ 1 & 3 & -1 & 1 & -1 & 1 & -1 & 0 \\ 1 & -1 & 3 & -1 & 1 & 1 & -1 & 0 \\ -1 & 1 & -1 & 3 & -1 & -1 & -1 & 0 \\ -1 & -1 & 1 & -1 & 3 & 1 & 1 & 0 \\ 1 & 1 & 1 & -1 & 1 & 3 & -1 & 0 \\ -1 & -1 & -1 & -1 & 1 & -1 & 3 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 4 \end{array}\right)$
	Download this matrix for gp, magma, sage