Integral lattice 8.256.4.1.5

• Label: 8.256.4.1.5
• Class number: $1$
• Dimension: $8$
• Determinant: $256$
• Level: $4$

Lattice Invariants

Dimension:

$8$

Determinant:

$256$

Level:

$4$

Density:

$0.0158543442438155008522852103985\dots$

Group order:

$1327104$

Hermite number:

$1.00000000000000000000000000000\dots$

Minimal vector length:

$2$

Kissing number:

$24$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrrr} 4 & 2 & -2 & -2 & 0 & 0 & 0 & 0 \\ 2 & 4 & 0 & 0 & 0 & 0 & 0 & 0 \\ -2 & 0 & 4 & 0 & 0 & 0 & 0 & 0 \\ -2 & 0 & 0 & 4 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 2 & 1 & -1 & -1 \\ 0 & 0 & 0 & 0 & 1 & 2 & -1 & -1 \\ 0 & 0 & 0 & 0 & -1 & -1 & 2 & 0 \\ 0 & 0 & 0 & 0 & -1 & -1 & 0 & 2 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrrr} 2 & 1 & 1 & -1 & 0 & 0 & 0 & 0 \\ 1 & 2 & 0 & -1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 2 & -1 & 0 & 0 & 0 & 0 \\ -1 & -1 & -1 & 2 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 4 & -2 & -2 & 2 \\ 0 & 0 & 0 & 0 & -2 & 4 & 2 & -2 \\ 0 & 0 & 0 & 0 & -2 & 2 & 4 & 0 \\ 0 & 0 & 0 & 0 & 2 & -2 & 0 & 4 \end{array}\right)$
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