Integral lattice 7.191102976.24.1.1

• Label: 7.191102976.24.1.1
• Class number: $1$
• Dimension: $7$
• Determinant: $191102976$
• Level: $24$

Lattice Invariants

Dimension:

$7$

Determinant:

$191102976$

Level:

$24$

Density:

$0.0159834662392313545527204668006\dots$

Group order:

$5760$

Hermite number:

$0.787305053129222826777609410214\dots$

Minimal vector length:

$12$

Kissing number:

$2$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrr} 12 & 6 & -6 & -6 & -6 & 6 & 6 \\ 6 & 15 & -3 & -3 & -3 & 3 & 3 \\ -6 & -3 & 23 & 7 & 7 & 1 & 1 \\ -6 & -3 & 7 & 23 & -1 & -7 & -7 \\ -6 & -3 & 7 & -1 & 23 & -7 & -7 \\ 6 & 3 & 1 & -7 & -7 & 23 & -1 \\ 6 & 3 & 1 & -7 & -7 & -1 & 23 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrr} 12 & 6 & 6 & -6 & -6 & -6 & 6 \\ 6 & 15 & 3 & -3 & -3 & -3 & 3 \\ 6 & 3 & 23 & 1 & -7 & -7 & -1 \\ -6 & -3 & 1 & 23 & 7 & 7 & 1 \\ -6 & -3 & -7 & 7 & 23 & -1 & -7 \\ -6 & -3 & -7 & 7 & -1 & 23 & -7 \\ 6 & 3 & -1 & 1 & -7 & -7 & 23 \end{array}\right)$
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