Smooth Fano Toric 5-folds with $\rho\leq2$
There are 16 varieties in this class:
| $(\dim,\#)$ | $\operatorname{rk} \mathrm{Pic}$ | $\operatorname{rk} K_0$ | Chambers | Cox degrees and $\Theta$-collection | Ext table |
|---|---|---|---|---|---|
| $(5,0)$ | 1 | 6 |
6: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 1\end{pmatrix}$ 6: $\begin{pmatrix}5 & 4 & 3 & 2 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 6 & 21 & 56 & 126 & 252 \\ 0 & 1 & 6 & 21 & 56 & 126 \\ 0 & 0 & 1 & 6 & 21 & 56 \\ 0 & 0 & 0 & 1 & 6 & 21 \\ 0 & 0 & 0 & 0 & 1 & 6 \\ 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,1)$ | 2 | 10 |
7: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 4 & 0 & 1\end{pmatrix}$ 13: $\begin{pmatrix}1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 8 & 7 & 6 & 5 & 4 & 4 & 3 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 5 & 15 & 35 & 70 & 71 & 126 & 131 & 210 & 225 & 330 & 365 & 565 \\ 0 & 1 & 5 & 15 & 35 & 35 & 70 & 71 & 126 & 131 & 210 & 225 & 365 \\ 0 & 0 & 1 & 5 & 15 & 15 & 35 & 35 & 70 & 71 & 126 & 131 & 225 \\ 0 & 0 & 0 & 1 & 5 & 5 & 15 & 15 & 35 & 35 & 70 & 71 & 131 \\ 0 & 0 & 0 & 0 & 1 & 1 & 5 & 5 & 15 & 15 & 35 & 35 & 71 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 0 & 15 & 0 & 35 & 70 \\ T^4 & 0 & 0 & 0 & 0 & T^4 & 1 & 1 & 5 & 5 & 15 & 15 & 35 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 0 & 15 & 35 \\ 5T^4 & T^4 & 0 & 0 & 0 & 5T^4 & 0 & T^4 & 1 & 1 & 5 & 5 & 15 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 15 \\ 15T^4 & 5T^4 & T^4 & 0 & 0 & 15T^4 & 0 & 5T^4 & 0 & T^4 & 1 & 1 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,19)$ | 2 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 3 & 3 & 0 & 1\end{pmatrix}$ 16: $\begin{pmatrix}2 & 2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 9 & 8 & 7 & 6 & 6 & 5 & 5 & 4 & 4 & 3 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 4 & 10 & 20 & 22 & 35 & 43 & 56 & 76 & 124 & 127 & 190 & 202 & 277 & 307 & 448 \\ 0 & 1 & 4 & 10 & 10 & 20 & 22 & 35 & 43 & 76 & 76 & 124 & 127 & 190 & 202 & 307 \\ 0 & 0 & 1 & 4 & 4 & 10 & 10 & 20 & 22 & 43 & 43 & 76 & 76 & 124 & 127 & 202 \\ 0 & 0 & 0 & 1 & 1 & 4 & 4 & 10 & 10 & 22 & 22 & 43 & 43 & 76 & 76 & 127 \\ 0 & 0 & 0 & 0 & 1 & 0 & 4 & 0 & 10 & 20 & 22 & 35 & 43 & 56 & 76 & 124 \\ T^3 & 0 & 0 & 0 & 2T^3 & 1 & 1 & 4 & 4 & 10 & 10+3T^3 & 22 & 22 & 43 & 43 & 76 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 10 & 10 & 20 & 22 & 35 & 43 & 76 \\ 4T^3 & T^3 & 0 & 0 & 8T^3 & 0 & 2T^3 & 1 & 1 & 4 & 4+12T^3 & 10 & 10+3T^3 & 22 & 22 & 43 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 4 & 4 & 10 & 10 & 20 & 22 & 43 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 4 & 4 & 10 & 10 & 22 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 0 & 10 & 20 \\ 0 & 0 & 0 & 0 & T^3 & 0 & 0 & 0 & 0 & 0 & 2T^3 & 1 & 1 & 4 & 4 & 10 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 10 \\ 0 & 0 & 0 & 0 & 4T^3 & 0 & T^3 & 0 & 0 & 0 & 8T^3 & 0 & 2T^3 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,48)$ | 2 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 2 & 0 & 1\end{pmatrix}$ 14: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 0 \\ 6 & 5 & 5 & 4 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 4 & 5 & 10 & 15 & 20 & 34 & 35 & 39 & 65 & 80 & 111 & 145 & 240 \\ 0 & 1 & 1 & 4 & 5 & 10 & 15 & 20 & 16 & 34 & 39 & 65 & 80 & 145 \\ 0 & 0 & 1 & 0 & 4 & 0 & 10 & 0 & 15 & 20 & 34 & 35 & 65 & 111 \\ 0 & 0 & 0 & 1 & 1 & 4 & 5 & 10 & 5 & 15 & 16 & 34 & 39 & 80 \\ 0 & 0 & 0 & 0 & 1 & 0 & 4 & 0 & 5 & 10 & 15 & 20 & 34 & 65 \\ 0 & 0 & T^3 & 0 & 0 & 1 & 1 & 4 & 1+T^3 & 5 & 5 & 15 & 16 & 39 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 4 & 5 & 10 & 15 & 34 \\ T^3 & 0 & 5T^3 & 0 & T^3 & 0 & 0 & 1 & 5T^3 & 1 & 1+T^3 & 5 & 5 & 16 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 0 & 10 & 20 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 4 & 5 & 15 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 10 \\ 0 & 0 & T^3 & 0 & 0 & 0 & 0 & 0 & T^3 & 0 & 0 & 1 & 1 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,206)$ | 2 | 12 |
7: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 2 & 2 & 2 & 0 & 1\end{pmatrix}$ 15: $\begin{pmatrix}3 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 1 & 0 & 0 \\ 8 & 7 & 6 & 6 & 5 & 5 & 4 & 4 & 3 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 3 & 6 & 9 & 10 & 19 & 33 & 39 & 51 & 69 & 109 & 119 & 159 & 189 & 279 \\ 0 & 1 & 3 & 3 & 6 & 9 & 19 & 19 & 33 & 39 & 69 & 69 & 109 & 119 & 189 \\ 0 & 0 & 1 & 1 & 3 & 3 & 9 & 9 & 19 & 19 & 39 & 39 & 69 & 69 & 119 \\ 0 & 0 & 0 & 1 & 0 & 3 & 6 & 9 & 10 & 19 & 33 & 39 & 51 & 69 & 109 \\ T^2 & 0 & 0 & 3T^2 & 1 & 1 & 3 & 3+6T^2 & 9 & 9 & 19 & 19+10T^2 & 39 & 39 & 69 \\ 0 & 0 & 0 & 0 & 0 & 1 & 3 & 3 & 6 & 9 & 19 & 19 & 33 & 39 & 69 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 3 & 3 & 9 & 9 & 19 & 19 & 39 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 & 6 & 9 & 10 & 19 & 33 \\ 0 & 0 & 0 & T^2 & 0 & 0 & 0 & 3T^2 & 1 & 1 & 3 & 3+6T^2 & 9 & 9 & 19 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 3 & 3 & 6 & 9 & 19 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 3 & 3 & 9 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 & 6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & T^2 & 0 & 0 & 0 & 3T^2 & 1 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,475)$ | 2 | 12 |
7: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$ 14: $\begin{pmatrix}3 & 2 & 3 & 2 & 3 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 2 & 3 & 8 & 6 & 13 & 18 & 33 & 32 & 48 & 63 & 98 & 103 & 168 \\ 0 & 1 & 0 & 3 & 0 & 8 & 6 & 18 & 10 & 33 & 32 & 63 & 50 & 103 \\ 0 & 0 & 1 & 2 & 3 & 3 & 8 & 13 & 18 & 18 & 33 & 48 & 63 & 98 \\ 0 & 0 & 0 & 1 & 0 & 2 & 3 & 8 & 6 & 13 & 18 & 33 & 32 & 63 \\ 0 & 2T^2 & 0 & 0 & 1 & 3T^2 & 2 & 3 & 8 & 4+4T^2 & 13 & 18 & 33 & 48 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 & 0 & 8 & 6 & 18 & 10 & 32 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 3 & 3 & 8 & 13 & 18 & 33 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 2 & 3 & 8 & 6 & 18 \\ 0 & T^2 & 0 & 0 & 0 & 2T^2 & 0 & 0 & 1 & 3T^2 & 2 & 3 & 8 & 13 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 & 0 & 6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 3 & 8 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 \\ 0 & 0 & 0 & 0 & 0 & T^2 & 0 & 0 & 0 & 2T^2 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,841)$ | 2 | 10 |
7: $\begin{pmatrix}0 & 1 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$ 10: $\begin{pmatrix}4 & 4 & 3 & 3 & 2 & 2 & 1 & 1 & 0 & 0 \\ 5 & 4 & 4 & 3 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 2 & 6 & 11 & 21 & 36 & 56 & 91 & 126 & 196 \\ 0 & 1 & 1 & 6 & 6 & 21 & 21 & 56 & 56 & 126 \\ 0 & 0 & 1 & 2 & 6 & 11 & 21 & 36 & 56 & 91 \\ 0 & 0 & 0 & 1 & 1 & 6 & 6 & 21 & 21 & 56 \\ 0 & 0 & 0 & 0 & 1 & 2 & 6 & 11 & 21 & 36 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 6 & 6 & 21 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 6 & 11 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,842)$ | 2 | 10 |
7: $\begin{pmatrix}0 & 0 & 0 & 0 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 3 & 0 & 1\end{pmatrix}$ 12: $\begin{pmatrix}1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 7 & 6 & 5 & 4 & 4 & 3 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 5 & 15 & 35 & 36 & 70 & 75 & 126 & 141 & 210 & 245 & 400 \\ 0 & 1 & 5 & 15 & 15 & 35 & 36 & 70 & 75 & 126 & 141 & 245 \\ 0 & 0 & 1 & 5 & 5 & 15 & 15 & 35 & 36 & 70 & 75 & 141 \\ 0 & 0 & 0 & 1 & 1 & 5 & 5 & 15 & 15 & 35 & 36 & 75 \\ 0 & 0 & 0 & 0 & 1 & 0 & 5 & 0 & 15 & 0 & 35 & 70 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 5 & 5 & 15 & 15 & 36 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 0 & 15 & 35 \\ T^4 & 0 & 0 & 0 & T^4 & 0 & 0 & 1 & 1 & 5 & 5 & 15 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 15 \\ 5T^4 & T^4 & 0 & 0 & 5T^4 & 0 & T^4 & 0 & 0 & 1 & 1 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,845)$ | 2 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 2 & 2 & 0 & 1\end{pmatrix}$ 14: $\begin{pmatrix}2 & 2 & 2 & 1 & 2 & 1 & 2 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 7 & 6 & 5 & 5 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 4 & 10 & 12 & 20 & 28 & 35 & 55 & 58 & 96 & 108 & 154 & 184 & 292 \\ 0 & 1 & 4 & 4 & 10 & 12 & 20 & 28 & 28 & 55 & 58 & 96 & 108 & 184 \\ 0 & 0 & 1 & 1 & 4 & 4 & 10 & 12 & 12 & 28 & 28 & 55 & 58 & 108 \\ 0 & 0 & 0 & 1 & 0 & 4 & 0 & 10 & 12 & 20 & 28 & 35 & 55 & 96 \\ 0 & 0 & 0 & 0 & 1 & 1 & 4 & 4 & 4 & 12 & 12 & 28 & 28 & 58 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 4 & 10 & 12 & 20 & 28 & 55 \\ T^3 & 0 & 0 & 2T^3 & 0 & 0 & 1 & 1 & 1+3T^3 & 4 & 4 & 12 & 12 & 28 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 4 & 4 & 10 & 12 & 28 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 0 & 10 & 20 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 4 & 4 & 12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 10 \\ 0 & 0 & 0 & T^3 & 0 & 0 & 0 & 0 & 2T^3 & 0 & 0 & 1 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,847)$ | 2 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 & 1 & 0 & 1\end{pmatrix}$ 13: $\begin{pmatrix}2 & 1 & 2 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 3 & 2 & 3 & 1 & 2 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 2 & 4 & 9 & 10 & 14 & 20 & 24 & 39 & 50 & 84 & 90 & 155 \\ 0 & 1 & 0 & 4 & 0 & 9 & 0 & 10 & 24 & 20 & 50 & 35 & 90 \\ 0 & 0 & 1 & 2 & 4 & 3 & 10 & 9 & 14 & 24 & 39 & 50 & 84 \\ 0 & 0 & 0 & 1 & 0 & 2 & 0 & 4 & 9 & 10 & 24 & 20 & 50 \\ 0 & 0 & 0 & 0 & 1 & 0 & 4 & 2 & 3 & 9 & 14 & 24 & 39 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 4 & 0 & 10 & 0 & 20 \\ 0 & T^3 & 0 & 0 & 0 & T^3 & 1 & 0 & 0 & 2 & 3 & 9 & 14 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 4 & 9 & 10 & 24 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 0 & 10 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 4 & 9 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 \\ 0 & T^3 & 0 & 0 & 0 & T^3 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,854)$ | 2 | 12 |
7: $\begin{pmatrix}0 & 0 & 1 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$ 12: $\begin{pmatrix}3 & 3 & 2 & 3 & 2 & 1 & 2 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 4 & 3 & 3 & 3 & 2 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 3 & 6 & 6 & 15 & 21 & 28 & 46 & 56 & 81 & 111 & 186 \\ 0 & 1 & 1 & 3 & 6 & 6 & 15 & 21 & 21 & 46 & 56 & 111 \\ 0 & 0 & 1 & 0 & 3 & 6 & 6 & 15 & 21 & 28 & 46 & 81 \\ 0 & 0 & 0 & 1 & 1 & 1 & 6 & 6 & 6 & 21 & 21 & 56 \\ 0 & 0 & 0 & 0 & 1 & 1 & 3 & 6 & 6 & 15 & 21 & 46 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 & 6 & 6 & 15 & 28 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 6 & 6 & 21 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 3 & 6 & 15 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 3 & 6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,860)$ | 2 | 10 |
7: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 2 & 0 & 1 & 1 & 1 & 1 & 1\end{pmatrix}$ 11: $\begin{pmatrix}1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 6 & 5 & 4 & 4 & 3 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 5 & 15 & 16 & 35 & 40 & 70 & 85 & 126 & 161 & 280 \\ 0 & 1 & 5 & 5 & 15 & 16 & 35 & 40 & 70 & 85 & 161 \\ 0 & 0 & 1 & 1 & 5 & 5 & 15 & 16 & 35 & 40 & 85 \\ 0 & 0 & 0 & 1 & 0 & 5 & 0 & 15 & 0 & 35 & 70 \\ 0 & 0 & 0 & 0 & 1 & 1 & 5 & 5 & 15 & 16 & 40 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 0 & 15 & 35 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 5 & 5 & 16 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 15 \\ T^4 & 0 & 0 & T^4 & 0 & 0 & 0 & 0 & 1 & 1 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,861)$ | 2 | 10 |
7: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 1 & 0 & 1 & 1 & 1 & 1 & 1\end{pmatrix}$ 10: $\begin{pmatrix}1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 4 & 3 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 5 & 6 & 15 & 20 & 35 & 50 & 70 & 105 & 196 \\ 0 & 1 & 1 & 5 & 6 & 15 & 20 & 35 & 50 & 105 \\ 0 & 0 & 1 & 0 & 5 & 0 & 15 & 0 & 35 & 70 \\ 0 & 0 & 0 & 1 & 1 & 5 & 6 & 15 & 20 & 50 \\ 0 & 0 & 0 & 0 & 1 & 0 & 5 & 0 & 15 & 35 \\ 0 & 0 & 0 & 0 & 0 & 1 & 1 & 5 & 6 & 20 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 15 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,862)$ | 2 | 10 |
7: $\begin{pmatrix}1 & 1 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 & 1\end{pmatrix}$ 10: $\begin{pmatrix}1 & 0 & 1 & 1 & 0 & 0 & 1 & 0 & 1 & 0 \\ 4 & 4 & 3 & 2 & 3 & 2 & 1 & 1 & 0 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 2 & 5 & 15 & 10 & 30 & 35 & 70 & 70 & 140 \\ 0 & 1 & 0 & 0 & 5 & 15 & 0 & 35 & 0 & 70 \\ 0 & 0 & 1 & 5 & 2 & 10 & 15 & 30 & 35 & 70 \\ 0 & 0 & 0 & 1 & 0 & 2 & 5 & 10 & 15 & 30 \\ 0 & 0 & 0 & 0 & 1 & 5 & 0 & 15 & 0 & 35 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 & 0 & 15 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 & 5 & 10 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 5 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 2 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,863)$ | 2 | 12 |
7: $\begin{pmatrix}0 & 0 & 0 & 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 1 & 1 & 0 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 2 & 1 & 2 & 1 & 2 & 0 & 1 & 0 & 1 & 0 & 0 \\ 5 & 4 & 4 & 3 & 3 & 2 & 3 & 2 & 2 & 1 & 1 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 4 & 6 & 10 & 18 & 20 & 21 & 40 & 52 & 75 & 105 & 186 \\ 0 & 1 & 1 & 4 & 6 & 10 & 6 & 18 & 21 & 40 & 52 & 105 \\ 0 & 0 & 1 & 0 & 4 & 0 & 6 & 10 & 18 & 20 & 40 & 75 \\ 0 & 0 & 0 & 1 & 1 & 4 & 1 & 6 & 6 & 18 & 21 & 52 \\ 0 & 0 & 0 & 0 & 1 & 0 & 1 & 4 & 6 & 10 & 18 & 40 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 1 & 1 & 6 & 6 & 21 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 0 & 10 & 20 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 4 & 6 & 18 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 10 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ | |
| $(5,864)$ | 2 | 12 |
7: $\begin{pmatrix}1 & 1 & 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 1 & 1 & 1 & 1\end{pmatrix}$ 12: $\begin{pmatrix}2 & 1 & 2 & 0 & 1 & 2 & 0 & 2 & 1 & 0 & 1 & 0 \\ 3 & 3 & 2 & 3 & 2 & 1 & 2 & 0 & 1 & 1 & 0 & 0\end{pmatrix}$ |
$\begin{pmatrix}1 & 3 & 4 & 6 & 12 & 10 & 24 & 20 & 30 & 60 & 60 & 120 \\ 0 & 1 & 0 & 3 & 4 & 0 & 12 & 0 & 10 & 30 & 20 & 60 \\ 0 & 0 & 1 & 0 & 3 & 4 & 6 & 10 & 12 & 24 & 30 & 60 \\ 0 & 0 & 0 & 1 & 0 & 0 & 4 & 0 & 0 & 10 & 0 & 20 \\ 0 & 0 & 0 & 0 & 1 & 0 & 3 & 0 & 4 & 12 & 10 & 30 \\ 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 & 3 & 6 & 12 & 24 \\ 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 4 & 0 & 10 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 3 & 6 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 3 & 4 & 12 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 4 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$ |