Integral lattice 3.64.128.2.1

• Label: 3.64.128.2.1
• Class number: $2$
• Dimension: $3$
• Determinant: $64$
• Level: $128$

Lattice Invariants

Dimension:

$3$

Determinant:

$64$

Level:

$128$

Density:

$0.185120122423265260292328374586\dots$

Group order:

$12$

Hermite number:

$0.500000000000000000000000000000\dots$

Minimal vector length:

$2$

Kissing number:

$6$

Normalized minimal vectors:

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

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Theta Series

Gram Matrix

$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 22 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$2$
$\left(\begin{array}{rrr} 2 & 1 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 22 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 6 & 1 \\ 0 & 1 & 6 \end{array}\right)$
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Comments

This lattice appears in the Brandt-Intrau-Schiemann Table of Even Ternary Quadratic Forms.