Integral lattice 7.34012224.18.1.1

• Label: 7.34012224.18.1.1
• Class number: $1$
• Dimension: $7$
• Determinant: $34012224$
• Level: $18$

Lattice Invariants

Dimension:

$7$

Determinant:

$34012224$

Level:

$18$

Density:

$0.00916574501273188471712377274224\dots$

Group order:

$7680$

Hermite number:

$0.671648618004179171418237382851\dots$

Minimal vector length:

$8$

Kissing number:

$2$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrr} 8 & -4 & -2 & 4 & -4 & 4 & 4 \\ -4 & 11 & 1 & -2 & 2 & -2 & -2 \\ -2 & 1 & 23 & -10 & -8 & -10 & 8 \\ 4 & -2 & -10 & 20 & -2 & 2 & 2 \\ -4 & 2 & -8 & -2 & 20 & -2 & -2 \\ 4 & -2 & -10 & 2 & -2 & 20 & 2 \\ 4 & -2 & 8 & 2 & -2 & 2 & 20 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrr} 8 & -4 & 4 & 4 & 2 & -2 & -2 \\ -4 & 11 & -2 & -2 & -1 & 1 & 1 \\ 4 & -2 & 20 & 2 & -8 & -10 & 8 \\ 4 & -2 & 2 & 20 & -8 & -10 & 8 \\ 2 & -1 & -8 & -8 & 23 & 13 & -5 \\ -2 & 1 & -10 & -10 & 13 & 23 & -13 \\ -2 & 1 & 8 & 8 & -5 & -13 & 23 \end{array}\right)$
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