Integral lattice 3.42.84.2.1

• Label: 3.42.84.2.1
• Class number: $2$
• Dimension: $3$
• Determinant: $42$
• Level: $84$

Lattice Invariants

Dimension:

$3$

Determinant:

$42$

Level:

$84$

Density:

$0.228517240282419179107439430628\dots$

Group order:

$24$

Hermite number:

$0.575369582664788042444646286707\dots$

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

$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 14 \end{array}\right)$

Genus Structure

Genus representatives:

Class number:	$2$
$\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 2 & 0 \\ 0 & 0 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & 0 \\ 1 & 4 & 0 \\ 0 & 0 & 6 \end{array}\right)$
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Comments

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