Integral lattice 8.5.5.1.1

• Label: 8.5.5.1.1
• Class number: $1$
• Dimension: $8$
• Determinant: $5$
• Level: $5$

Lattice Invariants

Dimension:

$8$

Determinant:

$5$

Level:

$5$

Density:

$0.113444452697132670874861585579\dots$

Group order:

$5806080$

Hermite number:

$1.63553086791588500914978052293\dots$

Minimal vector length:

$2$

Kissing number:

$126$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

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

Genus Structure

Genus representatives:

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