Integral lattice 6.2097152.64.1.1

• Label: 6.2097152.64.1.1
• Class number: $1$
• Dimension: $6$
• Determinant: $2097152$
• Level: $64$

Lattice Invariants

Dimension:

$6$

Determinant:

$2097152$

Level:

$64$

Density:

$0.0191248289375185812056523990872\dots$

Group order:

$240$

Hermite number:

$0.618718433538229083850738816841\dots$

Minimal vector length:

$7$

Kissing number:

$2$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrr} 7 & -3 & 3 & 3 & -3 & -3 \\ -3 & 15 & 1 & 1 & -1 & -1 \\ 3 & 1 & 15 & -1 & 1 & 1 \\ 3 & 1 & -1 & 15 & 1 & 1 \\ -3 & -1 & 1 & 1 & 15 & -1 \\ -3 & -1 & 1 & 1 & -1 & 15 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrr} 7 & -3 & 3 & 3 & -3 & -3 \\ -3 & 15 & 1 & 1 & -1 & -1 \\ 3 & 1 & 15 & -1 & 1 & 1 \\ 3 & 1 & -1 & 15 & 1 & 1 \\ -3 & -1 & 1 & 1 & 15 & -1 \\ -3 & -1 & 1 & 1 & -1 & 15 \end{array}\right)$
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