Lattice Invariants
Dimension: | $14$ |
Determinant: | $15$ |
Level: | $15$ |
Density: | $0.00120882371980846561842974135302\dots$ |
Group order: | $2615348736000$ |
Hermite number: | $1.64825149055779494991198141680\dots$ |
Minimal vector length: | $2$ |
Kissing number: | $210$ |
Normalized minimal vectors: |
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Theta Series
Gram Matrix
$\left(\begin{array}{rrrrrrrrrrrrrr} 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 & -1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & -1 & 2 \end{array}\right)$
Genus Structure
Class number: | $9$ |
$\left(\begin{array}{rrrrrrrrrrrrrr} 2 & 0 & -1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 1 & 1 & -1 & -1 \\ 0 & 2 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 & 0 & 0 \\ -1 & 0 & 2 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 2 & 1 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 1 & 2 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 1 & 1 & 2 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 1 \\ 0 & 1 & 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & -1 & 0 & 0 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 2 & 1 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 2 & 1 & -1 & -1 & 1 & 1 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 2 & -1 & -1 & 1 & 1 \\ 1 & 0 & -1 & -1 & -1 & -1 & 0 & -1 & -1 & -1 & 2 & 1 & -1 & -1 \\ 1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & -1 & 1 & 2 & -1 & -1 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 2 & 1 \\ -1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 & -1 & -1 & 1 & 2 \end{array}\right)$, $\left(\begin{array}{rrrrrrrrrrrrrr} 2 & 1 & 1 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ 1 & 2 & 0 & 0 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ 1 & 0 & 2 & -1 & 0 & 1 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ 0 & 0 & -1 & 2 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ 0 & 0 & 0 & 0 & 2 & 0 & 0 & 0 & 0 & -1 & -1 & 1 & 0 & -1 \\ 1 & 1 & 1 & 0 & 0 & 2 & -1 & 0 & 0 & 0 & 0 & 0 & -1 & 1 \\ -1 & -1 & -1 & 1 & 0 & -1 & 2 & 0 & 0 & 0 & 0 & 0 & 1 & -1 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 2 & 1 & -1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & -1 & 0 & 0 & 0 & -1 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 & -1 & -1 & 2 & 1 & -1 & 0 & 1 \\ 0 & 0 & 0 & 0 & -1 & 0 & 0 & 0 & 0 & 1 & 2 & -1 & 0 & 1 \\ 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & -1 & -1 & 2 & 0 & -1 \\ -1 & -1 & -1 & 1 & 0 & -1 & 1 & 0 & 0 & 0 & 0 & 0 & 2 & -1 \\ 1 & 1 & 1 & -1 & -1 & 1 & -1 & 0 & -1 & 1 & 1 & -1 & -1 & 4 \end{array}\right)$, $\left(\begin{array}{rrrrrrrrrrrrrr} 2 & -1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & 1 & -1 & -1 & -1 \\ -1 & 2 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 1 & -1 & 0 & 0 & 1 \\ 1 & -1 & 2 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & 1 & 0 & 0 & 0 \\ 1 & -1 & 1 & 2 & 1 & 1 & 1 & -1 & -1 & -1 & 1 & -1 & -1 & -1 \\ 1 & -1 & 1 & 1 & 2 & 1 & 1 & -1 & -1 & -1 & 1 & 0 & 0 & 0 \\ 1 & -1 & 1 & 1 & 1 & 2 & 1 & -1 & -1 & -1 & 1 & -1 & -1 & -1 \\ 1 & -1 & 1 & 1 & 1 & 1 & 2 & -1 & -1 & -1 & 1 & 0 & 0 & 0 \\ -1 & 1 & -1 & -1 & -1 & -1 & -1 & 2 & 1 & 1 & -1 & 1 & 1 & 1 \\ -1 & 1 & -1 & -1 & -1 & -1 & -1 & 1 & 2 & 1 & -1 & 1 & 1 & 1 \\ -1 & 1 & -1 & -1 & -1 & -1 & -1 & 1 & 1 & 2 & -1 & 0 & 0 & 1 \\ 1 & -1 & 1 & 1 & 1 & 1 & 1 & -1 & -1 & -1 & 2 & 0 & 0 & 0 \\ -1 & 0 & 0 & -1 & 0 & -1 & 0 & 1 & 1 & 0 & 0 & 4 & 3 & 2 \\ -1 & 0 & 0 & -1 & 0 & -1 & 0 & 1 & 1 & 0 & 0 & 3 & 4 & 2 \\ -1 & 1 & 0 & -1 & 0 & -1 & 0 & 1 & 1 & 1 & 0 & 2 & 2 & 4 \end{array}\right)$ ... | |
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Comments
This integral lattice is the A14 lattice.
This is a root lattice.