Integral lattice 7.729.6.1.1

• Label: 7.729.6.1.1
• Class number: $1$
• Dimension: $7$
• Determinant: $729$
• Level: $6$

Lattice Invariants

Dimension:

$7$

Determinant:

$729$

Level:

$6$

Density:

$0.0154671947089850554601463665025\dots$

Group order:

$46080$

Hermite number:

$0.779953875172457924308650483676\dots$

Minimal vector length:

$2$

Kissing number:

$6$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrrrrrr} 2 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 2 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 3 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 3 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 3 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 3 & 3 \\ 0 & 0 & 0 & 0 & 0 & 3 & 6 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$1$
$\left(\begin{array}{rrrrrrr} 2 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 2 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 3 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 3 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 3 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 3 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 3 \end{array}\right)$
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