Integral lattice 5.6.12.1.1 (A5)

• Name: A5
• Label: 5.6.12.1.1
• Class number: $1$
• Dimension: $5$
• Determinant: $6$
• Level: $12$

Lattice Invariants

Dimension:

$5$

Determinant:

$6$

Level:

$12$

Density:

$0.379881250517603758105399396698\dots$

Group order:

$1440$

Hermite number:

$1.39765423754315849046595420554\dots$

Minimal vector length:

$2$

Kissing number:

$30$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrr} 2 & -1 & 0 & 0 & 0 \\ -1 & 2 & -1 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & -1 & 2 & -1 \\ 0 & 0 & 0 & -1 & 2 \end{array}\right)$

Genus Structure

Genus representatives:

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

This integral lattice is the A5 lattice.

This is a root lattice.