Integral lattice 8.78125.5.1.1

• Label: 8.78125.5.1.1
• Class number: $1$
• Dimension: $8$
• Determinant: $78125$
• Level: $5$

Lattice Invariants

Dimension:

$8$

Determinant:

$78125$

Level:

$5$

Density:

$0.000907555621577061366998892684631\dots$

Group order:

$5806080$

Hermite number:

$0.489137817997540736776457745787\dots$

Minimal vector length:

$2$

Kissing number:

$2$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrrr} 2 & -1 & -1 & 1 & -1 & -1 & 1 & -1 \\ -1 & 8 & 3 & -3 & 3 & 3 & -3 & 3 \\ -1 & 3 & 8 & -3 & -2 & -2 & 2 & -2 \\ 1 & -3 & -3 & 8 & -3 & -3 & -2 & 2 \\ -1 & 3 & -2 & -3 & 8 & 3 & -3 & 3 \\ -1 & 3 & -2 & -3 & 3 & 8 & -3 & 3 \\ 1 & -3 & 2 & -2 & -3 & -3 & 8 & -3 \\ -1 & 3 & -2 & 2 & 3 & 3 & -3 & 8 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrrr} 2 & 1 & -1 & 1 & -1 & 1 & -1 & -1 \\ 1 & 8 & 2 & 3 & -3 & 3 & -3 & -3 \\ -1 & 2 & 8 & 2 & 3 & -3 & 3 & -2 \\ 1 & 3 & 2 & 8 & -3 & -2 & -3 & -3 \\ -1 & -3 & 3 & -3 & 8 & -3 & 3 & -2 \\ 1 & 3 & -3 & -2 & -3 & 8 & -3 & 2 \\ -1 & -3 & 3 & -3 & 3 & -3 & 8 & 3 \\ -1 & -3 & -2 & -3 & -2 & 2 & 3 & 8 \end{array}\right)$
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