Integral lattice 4.27648.288.1.1

• Label: 4.27648.288.1.1
• Class number: $1$
• Dimension: $4$
• Determinant: $27648$
• Level: $288$

Lattice Invariants

Dimension:

$4$

Determinant:

$27648$

Level:

$288$

Density:

$0.224441559143701439115006479495\dots$

Group order:

$4$

Hermite number:

$0.853054454176924632362783851401\dots$

Minimal vector length:

$11$

Kissing number:

$4$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrr} 11 & -3 & -4 & -1 \\ -3 & 11 & 4 & 1 \\ -4 & 4 & 16 & 4 \\ -1 & 1 & 4 & 19 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrr} 11 & -3 & -4 & -1 \\ -3 & 11 & 4 & 1 \\ -4 & 4 & 16 & 4 \\ -1 & 1 & 4 & 19 \end{array}\right)$
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