# Properties

 Label 3.1470.2940.10.2 Class number 10 Dimension 3 Determinant 1470 Level 2940

## Lattice Invariants

Dimension:$3$
Determinant:$1470$
Level:$2940$
Label:$3.1470.2940.10.2$
Density:$0.0386264635807010656852662930504\dots$
Group order:$4$
Hermite number:$0.175896642899793658528591029987\dots$
Minimal vector length:$2$
Kissing Number:$2$
Normalized minimal vectors: $(1, 0, 0)$

## Theta Series

$1$ $\mathstrut +\mathstrut 2q^{2}$ $\mathstrut +\mathstrut 2q^{8}$ $\mathstrut +\mathstrut 2q^{12}$ $\mathstrut +\mathstrut 4q^{14}$ $\mathstrut +\mathstrut 2q^{18}$ $\mathstrut +\mathstrut 4q^{20}$ $\mathstrut +\mathstrut O(q^{21})$

## Gram Matrix

$\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & 3 \\ 0 & 3 & 62 \end{array}\right)$

## Genus Structure

 Class number: $10$ Genus representatives: $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 12 & 3 \\ 0 & 3 & 62 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 3 & -1 \\ 3 & 12 & -3 \\ -1 & -3 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 8 & 2 & -1 \\ 2 & 10 & 2 \\ -1 & 2 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 1 & -1 \\ 1 & 10 & 4 \\ -1 & 4 & 80 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & -1 & 0 \\ -1 & 16 & -3 \\ 0 & -3 & 48 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 5 & -1 \\ 5 & 10 & 1 \\ -1 & 1 & 20 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & 1 & -2 \\ 1 & 8 & -4 \\ -2 & -4 & 50 \end{array}\right)$, $\left(\begin{array}{rrr} 10 & 4 & 4 \\ 4 & 14 & -1 \\ 4 & -1 & 14 \end{array}\right)$, $\left(\begin{array}{rrr} 2 & 0 & 0 \\ 0 & 20 & 5 \\ 0 & 5 & 38 \end{array}\right)$, $\left(\begin{array}{rrr} 4 & -1 & 1 \\ -1 & 14 & -4 \\ 1 & -4 & 28 \end{array}\right)$ Download this list for gp, magma, sage