Integral lattice 5.162.12.1.1

• Label: 5.162.12.1.1
• Class number: $1$
• Dimension: $5$
• Determinant: $162$
• Level: $12$

Lattice Invariants

Dimension:

$5$

Determinant:

$162$

Level:

$12$

Density:

$0.413562322941563231653781388810\dots$

Group order:

$1440$

Hermite number:

$1.44596236159693148499414656322\dots$

Minimal vector length:

$4$

Kissing number:

$30$

Normalized minimal vectors:

$(1, 0, 0, -1, -1)$, $(1, 0, 0, 0, -1)$, $(1, 0, 0, 0, 0)$, $(1, 0, 1, -1, -1)$, $(1, 1, 0, -1, -1)$, $(1, 1, 1, -1, -2)$, $(0, 1, 0, -1, -1)$, $(0, 1, 0, 0, -1)$, $(0, 1, 0, 0, 0)$, $(0, 1, 1, -1, -1)$, $(0, 0, 1, -1, -1)$, $(0, 0, 1, 0, -1)$, $(0, 0, 1, 0, 0)$, $(0, 0, 0, 1, 0)$, $(0, 0, 0, 0, 1)$ ...

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrr} 4 & 1 & 1 & 1 & 2 \\ 1 & 4 & 1 & 1 & 2 \\ 1 & 1 & 4 & 1 & 2 \\ 1 & 1 & 1 & 4 & -1 \\ 2 & 2 & 2 & -1 & 4 \end{array}\right)$

Genus Structure

Genus representatives:

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