Integral lattice 5.20736.24.1.1

• Label: 5.20736.24.1.1
• Class number: $1$
• Dimension: $5$
• Determinant: $20736$
• Level: $24$

Lattice Invariants

Dimension:

$5$

Determinant:

$20736$

Level:

$24$

Density:

$0.0638573679162815547174301193362\dots$

Group order:

$64$

Hermite number:

$0.684896595632177400961874140096\dots$

Minimal vector length:

$5$

Kissing number:

$4$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrr} 5 & -1 & -2 & 0 & 0 \\ -1 & 5 & -2 & 0 & 0 \\ -2 & -2 & 8 & 0 & 0 \\ 0 & 0 & 0 & 12 & 0 \\ 0 & 0 & 0 & 0 & 12 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrr} 5 & -1 & -2 & 0 & 0 \\ -1 & 5 & -2 & 0 & 0 \\ -2 & -2 & 8 & 0 & 0 \\ 0 & 0 & 0 & 12 & 0 \\ 0 & 0 & 0 & 0 & 12 \end{array}\right)$
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