% orbit 10, S = (0,0,2,0), degree 11
\begin{align*}
x &= m^{11} - 12m^{10}n + 74m^{9}n^{2} - 304m^{8}n^{3} + 883m^{7}n^{4} - 1768m^{6}n^{5}\\
&\quad  + 2237m^{5}n^{6} - 1306m^{4}n^{7} - 674m^{3}n^{8} + 1818m^{2}n^{9} - 1269mn^{10} + 324n^{11},\\
y &= 3m^{10}n - 34m^{9}n^{2} + 186m^{8}n^{3} - 640m^{7}n^{4} + 1531m^{6}n^{5} - 2724m^{5}n^{6}\\
&\quad  + 3831m^{4}n^{7} - 4384m^{3}n^{8} + 3850m^{2}n^{9} - 2214mn^{10} + 603n^{11},\\
z &= m^{11} - 13m^{10}n + 70m^{9}n^{2} - 194m^{8}n^{3} + 219m^{7}n^{4} + 321m^{6}n^{5}\\
&\quad  - 1695m^{5}n^{6} + 3185m^{4}n^{7} - 3564m^{3}n^{8} + 2624m^{2}n^{9} - 1275mn^{10} + 333n^{11},\\
u &= -5m^{10}n + 58m^{9}n^{2} - 298m^{8}n^{3} + 886m^{7}n^{4} - 1619m^{6}n^{5} + 1660m^{5}n^{6}\\
&\quad  - 277m^{4}n^{7} - 1848m^{3}n^{8} + 2866m^{2}n^{9} - 2004mn^{10} + 585n^{11},\\
v &= -m^{11} + 11m^{10}n - 52m^{9}n^{2} + 108m^{8}n^{3} + 55m^{7}n^{4} - 921m^{6}n^{5}\\
&\quad  + 2571m^{5}n^{6} - 3907m^{4}n^{7} + 3518m^{3}n^{8} - 1670m^{2}n^{9} + 165mn^{10} + 135n^{11},\\
w &= m^{11} - 14m^{10}n + 82m^{9}n^{2} - 280m^{8}n^{3} + 657m^{7}n^{4} - 1248m^{6}n^{5}\\
&\quad  + 2233m^{5}n^{6} - 3708m^{4}n^{7} + 4850m^{3}n^{8} - 4278m^{2}n^{9} + 2181mn^{10} - 468n^{11}.
\end{align*}