Integral lattice 7.2985984.12.1.1

• Label: 7.2985984.12.1.1
• Class number: $1$
• Dimension: $7$
• Determinant: $2985984$
• Level: $12$

Lattice Invariants

Dimension:

$7$

Determinant:

$2985984$

Level:

$12$

Density:

$0.0309343894179701109202927330051\dots$

Group order:

$46080$

Hermite number:

$0.950774423484919226989413790301\dots$

Minimal vector length:

$8$

Kissing number:

$6$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrr} 12 & 0 & 6 & -6 & -6 & 0 & 0 \\ 0 & 12 & 6 & -6 & -6 & 0 & 0 \\ 6 & 6 & 15 & -9 & -9 & 0 & 0 \\ -6 & -6 & -9 & 15 & 3 & 0 & 0 \\ -6 & -6 & -9 & 3 & 15 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 8 & -4 \\ 0 & 0 & 0 & 0 & 0 & -4 & 8 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrr} 8 & -4 & 0 & 0 & 0 & 0 & 0 \\ -4 & 8 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 12 & 0 & -6 & 6 & -6 \\ 0 & 0 & 0 & 12 & -6 & 6 & -6 \\ 0 & 0 & -6 & -6 & 15 & -9 & 3 \\ 0 & 0 & 6 & 6 & -9 & 15 & -9 \\ 0 & 0 & -6 & -6 & 3 & -9 & 15 \end{array}\right)$
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