Integral lattice 5.8957952.72.1.1

• Label: 5.8957952.72.1.1
• Class number: $1$
• Dimension: $5$
• Determinant: $8957952$
• Level: $72$

Lattice Invariants

Dimension:

$5$

Determinant:

$8957952$

Level:

$72$

Density:

$0.0478930259372111660380725895021\dots$

Group order:

$16$

Hermite number:

$0.610449177413233656381109732817\dots$

Minimal vector length:

$15$

Kissing number:

$2$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrr} 15 & -3 & 3 & 6 & -6 \\ -3 & 23 & -7 & 10 & -2 \\ 3 & -7 & 23 & -2 & 10 \\ 6 & 10 & -2 & 44 & -4 \\ -6 & -2 & 10 & -4 & 44 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrr} 15 & -3 & 3 & 6 & -6 \\ -3 & 23 & -7 & 10 & -2 \\ 3 & -7 & 23 & -2 & 10 \\ 6 & 10 & -2 & 44 & -4 \\ -6 & -2 & 10 & -4 & 44 \end{array}\right)$
	Download this matrix for gp, magma, sage