Select desired size of Galois group. Note that the following data has not all been computed for fields in this family, so the tables below are incomplete.
Label |
Packet size |
Polynomial |
Galois group |
Galois degree |
$\#\Aut(K/\Q_p)$ |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
2.1.16.64j1.1025 |
|
$x^{16} + 2 x^{8} + 8 x^{6} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1026 |
|
$x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1027 |
|
$x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1028 |
|
$x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1029 |
|
$x^{16} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1030 |
|
$x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1031 |
|
$x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1032 |
|
$x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1033 |
|
$x^{16} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$C_2^6:(C_2\times C_4)$ (as 16T865) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1034 |
|
$x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$C_2^6:(C_2\times C_4)$ (as 16T865) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1035 |
|
$x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$C_2^6:(C_2\times C_4)$ (as 16T865) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1036 |
|
$x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$C_2^6:(C_2\times C_4)$ (as 16T865) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1037 |
|
$x^{16} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1038 |
|
$x^{16} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1039 |
|
$x^{16} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1040 |
|
$x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1041 |
|
$x^{16} + 2 x^{8} + 8 x^{6} + 16 x^{2} + 16 x + 6$ |
$C_2^4.(C_4\times D_4)$ (as 16T847) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1042 |
|
$x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{2} + 16 x + 6$ |
$C_2^4.(C_4\times D_4)$ (as 16T847) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1043 |
|
$x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{2} + 16 x + 6$ |
$C_2^4.(C_4\times D_4)$ (as 16T847) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1044 |
|
$x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{2} + 16 x + 6$ |
$C_2^4.(C_4\times D_4)$ (as 16T847) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1045 |
|
$x^{16} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{2} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1046 |
|
$x^{16} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{2} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1047 |
|
$x^{16} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{2} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1048 |
|
$x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{2} + 16 x + 6$ |
$C_2^6:Q_8$ (as 16T973) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1049 |
|
$x^{16} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x^{2} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1050 |
|
$x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x^{2} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1051 |
|
$x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x^{2} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1052 |
|
$x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x^{2} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1053 |
|
$x^{16} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x^{2} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1054 |
|
$x^{16} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x^{2} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1055 |
|
$x^{16} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x^{2} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1056 |
|
$x^{16} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x^{3} + 16 x^{2} + 16 x + 6$ |
$(C_2^2\times C_4^2):Q_8$ (as 16T950) |
$512$ |
$2$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,3,4,4]^{2}$ |
$[2,2,3,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1057 |
|
$x^{16} + 8 x^{14} + 2 x^{8} + 8 x^{6} + 16 x + 6$ |
$C_4^2:D_4$ (as 16T365) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1058 |
|
$x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x + 6$ |
$C_4^2:D_4$ (as 16T365) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1059 |
|
$x^{16} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x + 6$ |
$C_4^2:D_4$ (as 16T399) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1060 |
|
$x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x + 6$ |
$C_4^2:D_4$ (as 16T399) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1061 |
|
$x^{16} + 8 x^{14} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 6$ |
$C_2^6:D_4$ (as 16T960) |
$512$ |
$2$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,3,\frac{7}{2},4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1062 |
|
$x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 6$ |
$C_2^6:D_4$ (as 16T960) |
$512$ |
$2$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,3,\frac{7}{2},4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1063 |
|
$x^{16} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 6$ |
$C_2^6:D_4$ (as 16T960) |
$512$ |
$2$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,3,\frac{7}{2},4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1064 |
|
$x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x + 6$ |
$C_2^6:D_4$ (as 16T960) |
$512$ |
$2$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,3,\frac{7}{2},4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1065 |
|
$x^{16} + 8 x^{14} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2\wr D_4$ (as 16T395) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1066 |
|
$x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2\wr D_4$ (as 16T395) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1067 |
|
$x^{16} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_4^2:D_4$ (as 16T341) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1068 |
|
$x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_4^2:D_4$ (as 16T341) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1069 |
|
$x^{16} + 8 x^{14} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2^6:D_4$ (as 16T960) |
$512$ |
$2$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,3,\frac{7}{2},4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1070 |
|
$x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2^6:D_4$ (as 16T960) |
$512$ |
$2$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,3,\frac{7}{2},4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1071 |
|
$x^{16} + 8 x^{14} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2^6:D_4$ (as 16T960) |
$512$ |
$2$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,3,\frac{7}{2},4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1072 |
|
$x^{16} + 8 x^{14} + 16 x^{12} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{4} + 16 x + 6$ |
$C_2^6:D_4$ (as 16T960) |
$512$ |
$2$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,3,\frac{7}{2},4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1073 |
|
$x^{16} + 8 x^{14} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$C_2\wr D_4$ (as 16T395) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
2.1.16.64j1.1074 |
|
$x^{16} + 8 x^{14} + 16 x^{12} + 2 x^{8} + 8 x^{6} + 16 x^{3} + 16 x + 6$ |
$C_2\wr D_4$ (as 16T395) |
$128$ |
$2$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[3,4]^{2}$ |
$[2,3]^{2}$ |
$[49, 38, 24, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |