Integral lattice 7.1000000.10.1.1

• Label: 7.1000000.10.1.1
• Class number: $1$
• Dimension: $7$
• Determinant: $1000000$
• Level: $10$

Lattice Invariants

Dimension:

$7$

Determinant:

$1000000$

Level:

$10$

Density:

$0.00472476597033140116959639086737\dots$

Group order:

$46080$

Hermite number:

$0.555798197749255054851994086941\dots$

Minimal vector length:

$4$

Kissing number:

$2$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrr} 4 & -2 & 0 & 2 & -2 & 2 & -2 \\ -2 & 11 & -5 & -1 & 1 & -1 & 1 \\ 0 & -5 & 15 & -5 & -5 & -5 & 5 \\ 2 & -1 & -5 & 11 & -1 & 1 & -1 \\ -2 & 1 & -5 & -1 & 11 & -1 & 1 \\ 2 & -1 & -5 & 1 & -1 & 11 & -1 \\ -2 & 1 & 5 & -1 & 1 & -1 & 11 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrr} 4 & 2 & -2 & 2 & 0 & -2 & -2 \\ 2 & 11 & -1 & 1 & -5 & -6 & 4 \\ -2 & -1 & 11 & -1 & -5 & -4 & 6 \\ 2 & 1 & -1 & 11 & -5 & -6 & 4 \\ 0 & -5 & -5 & -5 & 15 & 10 & -10 \\ -2 & -6 & -4 & -6 & 10 & 16 & -4 \\ -2 & 4 & 6 & 4 & -10 & -4 & 16 \end{array}\right)$
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