Integral lattice 8.1024.4.1.2

• Label: 8.1024.4.1.2
• Class number: $1$
• Dimension: $8$
• Determinant: $1024$
• Level: $4$

Lattice Invariants

Dimension:

$8$

Determinant:

$1024$

Level:

$4$

Density:

$0.00792717212190775042614260519925\dots$

Group order:

$184320$

Hermite number:

$0.840896415253714543031125476233\dots$

Minimal vector length:

$2$

Kissing number:

$12$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrrr} 2 & 1 & -1 & 0 & 0 & -1 & 1 & -1 \\ 1 & 2 & -1 & 0 & 0 & -1 & 1 & -1 \\ -1 & -1 & 2 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 4 & 0 & 2 & -2 & 2 \\ 0 & 0 & 0 & 0 & 4 & 2 & -2 & 2 \\ -1 & -1 & 0 & 2 & 2 & 6 & -4 & 4 \\ 1 & 1 & 0 & -2 & -2 & -4 & 6 & -2 \\ -1 & -1 & 0 & 2 & 2 & 4 & -2 & 6 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrrr} 2 & -1 & 1 & 0 & 0 & 0 & 0 & 0 \\ -1 & 2 & -1 & 0 & 0 & -1 & 1 & -1 \\ 1 & -1 & 2 & 0 & 0 & 1 & -1 & 1 \\ 0 & 0 & 0 & 4 & 0 & 2 & -2 & 2 \\ 0 & 0 & 0 & 0 & 4 & 2 & -2 & 2 \\ 0 & -1 & 1 & 2 & 2 & 6 & -4 & 4 \\ 0 & 1 & -1 & -2 & -2 & -4 & 6 & -2 \\ 0 & -1 & 1 & 2 & 2 & 4 & -2 & 6 \end{array}\right)$
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