# Properties

 Label 3.706.1412.19.14 Class number 19 Dimension 3 Determinant 706 Level 1412

## Lattice Invariants

Dimension:$3$
Determinant:$706$
Level:$1412$
Label:$3.706.1412.19.14$
Density:$0.289616397670481146418560497894\dots$
Group order:$2$
Hermite number:$0.673828977216881115012713824306\dots$
Minimal vector length:$6$
Kissing number:$2$
Normalized minimal vectors: $(1, 0, 0)$

## Theta Series

$1$ $\mathstrut +\mathstrut 2q^{6}$ $\mathstrut +\mathstrut 2q^{8}$ $\mathstrut +\mathstrut 4q^{14}$ $\mathstrut +\mathstrut 2q^{16}$ $\mathstrut +\mathstrut 2q^{18}$ $\mathstrut +\mathstrut 2q^{20}$ $\mathstrut +\mathstrut O(q^{21})$

## Gram Matrix

$\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 8 & 3 \\ 1 & 3 & 16 \end{array}\right)$

## Genus Structure

 Class number: $19$ Genus representatives: $\left(\begin{array}{rrr} 6 & 0 & 1 \\ 0 & 8 & 3 \\ 1 & 3 & 16 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & -1 \\ -1 & 8 & 3 \\ -1 & 3 & 24 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 0 & 1 \\ 0 & 10 & 1 \\ 1 & 1 & 18 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & -1 \\ 0 & 12 & 5 \\ -1 & 5 & 32 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & -3 & 3 \\ -3 & 10 & -4 \\ 3 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -2 & 1 \\ -2 & 14 & -2 \\ 1 & -2 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 1 & 3 \\ 1 & 10 & -4 \\ 3 & -4 & 12 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 14 & -2 \\ 1 & -2 & 26 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 1 \\ 0 & 12 & -1 \\ 1 & -1 & 30 \end{array}\right)$ ... Download the complete list for gp, magma, sage