Theorem 1.2(i), independent orbit computation on A(F_q) = E(F_q)^2, E: y^2 = x^3 - x
  p  n    q   #E      pi  #orbits #ideals|mu   #Y!=0     #ok  #pi(Y)=Y
  5  1    5    8  -1-2i        4          4      63      63        63
  5  2   25   32  -1-2i        6          6    1023    1023        63
  5  3  125  104  -1-2i        8          8   10815   10815        63
  5  4  625  640  -1-2i       16         16  409599  409599        63
 13  1   13    8   3+2i        4          4      63      63        63
 13  2  169  160   3+2i       12         12   25599   25599        63
 17  1   17   16   1+4i        5          5     255     255       255
 17  2  289  320   1+4i       14         14  102399  102399       255
 29  1   29   40  -5-2i        8          8    1599    1599      1599
 29  2  841  800  -5-2i       24         24  639999  639999      1599
 37  1   37   40  -1-6i        8          8    1599    1599      1599
 41  1   41   32   5+4i        6          6    1023    1023      1023
 53  1   53   40   7+2i        8          8    1599    1599      1599
 61  1   61   72  -5+6i        8          8    5183    5183      5183
 73  1   73   80  -3-8i       10         10    6399    6399      6399
 89  1   89   80   5-8i       10         10    6399    6399      6399
 97  1   97   80   9+4i       10         10    6399    6399      6399
TOTAL: 17 fields, 1220015 nonzero points Y, pi(Y) in the SL_2(Z[i])-orbit of Y for 1220015
E(F_q) is a cyclic Z[i]-module with #E(F_q) = N(pi^n - 1) in every case; orbit counts match
