| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.2.8.56a5.265 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.266 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 16 t x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.267 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.268 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 16 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.269 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.270 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 16 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.271 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.272 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 16 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.273 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.274 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 8 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.275 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.276 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 8 x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.277 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 8\right) x^{4} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.278 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 8 x^{4} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.279 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.280 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 8 x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1033 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 12\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1034 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 12 x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1035 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 12\right) x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1036 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 12 x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1037 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 12\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1038 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 12 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1039 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 12\right) x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1040 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 12 x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1081 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 12 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1082 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 4\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1083 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 12 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1084 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 4\right) x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1085 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 12 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1086 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 4\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1087 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 12 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1088 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 4\right) x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1121 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 4\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1122 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1123 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 4\right) x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1124 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1125 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 4\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1126 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1127 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 4\right) x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1128 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1137 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 12 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 12 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1138 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 12\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1139 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 12 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 12 x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1140 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 12\right) x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1141 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 12 ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 12 x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1142 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 12\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 12\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1143 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 12 ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 12 x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1144 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 12\right) x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1161 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 12\right) x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1162 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{31}{8}, \frac{9}{2}]^{4}$ |
$[1,1,2,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8},\frac{7}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2},\frac{15}{4},\frac{31}{8}]^{2}$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{23}{8}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 12 x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
