Integral lattice 5.2560000.40.1.1

• Label: 5.2560000.40.1.1
• Class number: $1$
• Dimension: $5$
• Determinant: $2560000$
• Level: $40$

Lattice Invariants

Dimension:

$5$

Determinant:

$2560000$

Level:

$40$

Density:

$0.122504154092806571497168801887\dots$

Group order:

$48$

Hermite number:

$0.888793619702582246055037497536\dots$

Minimal vector length:

$17$

Kissing number:

$4$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrr} 20 & 10 & -10 & 10 & -10 \\ 10 & 17 & -9 & 9 & -5 \\ -10 & -9 & 33 & 7 & 5 \\ 10 & 9 & 7 & 33 & -5 \\ -10 & -5 & 5 & -5 & 25 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrr} 17 & -7 & -5 & -8 & 8 \\ -7 & 17 & -5 & 8 & -8 \\ -5 & -5 & 25 & 0 & 0 \\ -8 & 8 & 0 & 32 & 8 \\ 8 & -8 & 0 & 8 & 32 \end{array}\right)$
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