| 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 |
| 2.2.6.12a1.1 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 x ( x^{2} + x + 1 )^{2} + 2 x ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$12$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}]_{3}^{12}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]_{3}^{12}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{6}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{2} + 2 t x + 2 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 7]$ |
| 2.2.6.12a1.2 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 x ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$12$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x + 2 t$ |
$[1, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 7]$ |
| 2.2.6.12a1.3 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$6$ |
$12$ |
$S_4$ (as 12T9) |
$2$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{2}$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x + 2$ |
$[1, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 7]$ |
| 2.2.6.12a1.4 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 x ( x^{2} + x + 1 )^{2} + 2 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$6$ |
$12$ |
$A_4:C_4$ (as 12T30) |
$4$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{4}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 7]$ |
| 2.2.6.16a1.1 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2]_{3}^{6}$ |
$[1,1]_{3}^{6}$ |
$[2]^{3}$ |
$[1]^{3}$ |
$6$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{3} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.16a1.2 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x + 4$ |
$2$ |
$2$ |
$6$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2]_{3}^{6}$ |
$[1,1]_{3}^{6}$ |
$[2]^{3}$ |
$[1]^{3}$ |
$6$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{3} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.16a1.3 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 t x^{3} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.16a1.4 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x + 4$ |
$2$ |
$2$ |
$6$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 t x^{3} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.16a1.5 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$D_6$ (as 12T3) |
$2$ |
$3$ |
$[2]$ |
$[1]$ |
$[2]_{3}^{2}$ |
$[1]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 6]$ |
| 2.2.6.16a1.6 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{3} + 4 x + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$C_3 : C_4$ (as 12T5) |
$2$ |
$3$ |
$[2]$ |
$[1]$ |
$[2]_{3}^{2}$ |
$[1]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{3} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 12]$ |
| 2.2.6.16a1.7 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$C_2\times S_4$ (as 12T21) |
$2$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3}]$ |
$[\frac{1}{3},\frac{1}{3}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 11]$ |
| 2.2.6.16a1.8 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 4 x + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$A_4:C_4$ (as 12T30) |
$2$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3}]$ |
$[\frac{1}{3},\frac{1}{3}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 4 t + 2$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 11]$ |
| 2.2.6.16a2.1 |
$12$ |
$( x^{2} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$16$ |
$C_6\times S_3$ (as 12T18) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2]_{3}^{6}$ |
$[1]_{3}^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{3} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 6]$ |
| 2.2.6.16a2.2 |
$12$ |
$( x^{2} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x + 4$ |
$2$ |
$2$ |
$6$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2]_{3}^{6}$ |
$[1]_{3}^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t^{2} + t + 1$ |
$x^{6} + \left(2 t + 2\right) x^{3} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 12]$ |
| 2.2.6.16a2.3 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$16$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(2 t + 2\right) x^{3} + 2 t + 4$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 11]$ |
| 2.2.6.16a2.4 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x + 4$ |
$2$ |
$2$ |
$6$ |
$16$ |
$A_4^2:C_2^2$ (as 12T158) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + \left(2 t + 2\right) x^{3} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 11]$ |
| 2.2.6.16a2.5 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3},2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 t x^{3} + 2$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 9]$ |
| 2.2.6.16a2.6 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$6$ |
$16$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T50) |
$2$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3},2]$ |
$[\frac{1}{3},\frac{1}{3},1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 t x^{3} + 6$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 9]$ |
| 2.2.6.16a2.7 |
$12$ |
$( x^{2} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2]_{3}^{2}$ |
$[1,1]_{3}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{3} + 6$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 9]$ |
| 2.2.6.16a2.8 |
$12$ |
$( x^{2} + x + 1 )^{6} + \left(2 x + 2\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$6$ |
$16$ |
$(C_6\times C_2):C_2$ (as 12T15) |
$2$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2]_{3}^{2}$ |
$[1,1]_{3}^{2}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{3} + 2$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 9]$ |
| 2.2.6.16a2.9 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 6 x + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 9]$ |
| 2.2.6.16a2.10 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2]_{3}^{6}$ |
$[1,1]_{3}^{6}$ |
$[2]^{3}$ |
$[1]^{3}$ |
$6$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{3} + 2 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 9]$ |
| 2.2.6.16a2.11 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 6 x + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$C_6\wr C_2$ (as 12T42) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[2, 2]_{3}^{6}$ |
$[1,1]_{3}^{6}$ |
$[2]^{3}$ |
$[1]^{3}$ |
$6$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{3} + 6 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 9]$ |
| 2.2.6.16a2.12 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x + 2$ |
$2$ |
$2$ |
$6$ |
$16$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[2]$ |
$[1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3},2]^{3}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 x^{5} + 2 x^{3} + 6 t$ |
$[3, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + t$ |
$[3, 9]$ |
| 2.2.6.20a1.1 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{12}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{12}$ |
$[\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{6}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{6}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + \left(4 t + 4\right) x^{3} + 4 x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.2 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{3} + 4 x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.3 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 t x^{3} + 4 x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.4 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{12}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{12}$ |
$[\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{6}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{6}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + 4 x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.5 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(4 x + 2\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 4\right) x^{3} + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.6 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(4 x + 2\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + \left(4 t + 4\right) x^{3} + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.7 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + \left(4 x + 2\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + 4 x^{3} + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.8 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{3} + \left(4 x + 2\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{3} + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.9 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 2\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + 4 t x^{3} + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.10 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 2\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 t x^{3} + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.11 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 2\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.12 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 2\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.13 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 4\right) x^{3} + 4 x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.14 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{12}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{12}$ |
$[\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{6}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{6}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + 4 x^{3} + 4 x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.15 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$12$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{12}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{12}$ |
$[\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{6}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{6}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + 4 t x^{3} + 4 x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.16 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4\wr C_2$ (as 12T126) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[\frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.17 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 6 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{3} + 4 t x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.18 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 6 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + 4 x^{3} + 4 t x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.19 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{3} + 6 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + \left(4 t + 4\right) x^{3} + 4 t x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.20 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 6 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 4\right) x^{3} + 4 t x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.21 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + 6 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + 4 t x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.22 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 6 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 t x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.23 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 6 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 t x^{3} + 4 t x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.24 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 6 ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:D_4$ (as 12T208) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, 2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + 4 t x^{3} + 4 t x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.25 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 6\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:C_2^2$ (as 12T158) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + \left(4 t + 4\right) x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
| 2.2.6.20a1.26 |
$12$ |
$( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 6\right) ( x^{2} + x + 1 ) + 2 x$ |
$2$ |
$2$ |
$6$ |
$20$ |
$A_4^2:C_4$ (as 12T159) |
$6$ |
$3$ |
$[\frac{8}{3}]$ |
$[\frac{5}{3}]$ |
$[2, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}, \frac{8}{3}]_{3}^{6}$ |
$[1,\frac{5}{3},\frac{5}{3},\frac{5}{3},\frac{5}{3}]_{3}^{6}$ |
$[2,\frac{8}{3},\frac{8}{3},\frac{8}{3}]^{3}$ |
$[1,\frac{5}{3},\frac{5}{3},\frac{5}{3}]^{3}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{6} + 2 t x^{5} + 4 x^{4} + \left(4 t + 4\right) x + 2 t$ |
$[5, 0]$ |
$[1, 1]$ |
$z^4 + z^2 + 1,z + 1$ |
$[3, 9]$ |
