# Properties

 Label 3.94.188.5.1 Class number 5 Dimension 3 Determinant 94 Level 188

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## Lattice Invariants

Dimension:$3$
Determinant:$94$
Level:$188$
Label:$3.94.188.5.1$
Density:$0.152749461901907729113327652429\dots$
Group order:$8$
Hermite number:$0.439866321268436508309298157756\dots$
Minimal vector length:$2$
Kissing Number:$4$
Normalized minimal vectors: $(1, 0, 0)$, $(0, 1, 0)$
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## Theta Series

$1$ $\mathstrut +\mathstrut 4q^{2}$ $\mathstrut +\mathstrut 4q^{4}$ $\mathstrut +\mathstrut 4q^{8}$ $\mathstrut +\mathstrut 8q^{10}$ $\mathstrut +\mathstrut 4q^{16}$ $\mathstrut +\mathstrut 4q^{18}$ $\mathstrut +\mathstrut 8q^{20}$ $\mathstrut +\mathstrut O(q^{21})$

## Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 24 \end{array}\right)$

## Genus Structure

 Class number: $5$ Genus representatives: $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 2 & 0 \\ 1 & 0 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 4 & 1 \\ 0 & 1 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 4 & -1 \\ -1 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 6 & -1 \\ 0 & -1 & 8 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & -1 \\ -1 & 2 & 1 \\ -1 & 1 & 32 \end{array}\right)$ Download this list for gp, magma, sage

## Comments

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