Integral lattice 6.48.12.1.1

• Label: 6.48.12.1.1
• Class number: $1$
• Dimension: $6$
• Determinant: $48$
• Level: $12$

Lattice Invariants

Dimension:

$6$

Determinant:

$48$

Level:

$12$

Density:

$0.0932368863955162348908693896698\dots$

Group order:

$768$

Hermite number:

$1.04911506342164818552752148969\dots$

Minimal vector length:

$2$

Kissing number:

$16$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

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

Genus Structure

Genus representatives:

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