| 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 |
| 3.1.12.21a1.1 |
$12$ |
$x^{12} + 6 x^{10} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.2 |
$12$ |
$x^{12} + 6 x^{10} + 9 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 9 x^{2} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.3 |
$12$ |
$x^{12} + 6 x^{10} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 18 x^{2} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.4 |
$12$ |
$x^{12} + 6 x^{10} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},\frac{9}{4}]^{2}$ |
$[\frac{1}{2},\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 9 x + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.5 |
$12$ |
$x^{12} + 6 x^{10} + 9 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},\frac{9}{4}]^{2}$ |
$[\frac{1}{2},\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 9 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.6 |
$12$ |
$x^{12} + 6 x^{10} + 18 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},\frac{9}{4}]^{2}$ |
$[\frac{1}{2},\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 6 x^{10} + 18 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.7 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.8 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{2} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.9 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{2} + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.10 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 9 x + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.11 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 9 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.12 |
$12$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 6 x^{10} + 18 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.13 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[2,\frac{9}{4}]^{2}$ |
$[1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 9 x + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.14 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 9 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[2,\frac{9}{4}]^{2}$ |
$[1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 9 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.15 |
$12$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 18 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[2,\frac{9}{4}]^{2}$ |
$[1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 6 x^{10} + 18 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
$[2, 14]$ |
| 3.1.12.21a1.16 |
$12$ |
$x^{12} + 3 x^{10} + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.17 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.18 |
$12$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.19 |
$12$ |
$x^{12} + 3 x^{10} + 9 x + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},\frac{9}{4}]^{2}$ |
$[\frac{1}{2},\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.20 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 9 x + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},\frac{9}{4}]^{2}$ |
$[\frac{1}{2},\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 9 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.21 |
$12$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 9 x + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:S_3$ (as 12T120) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},\frac{9}{4}]^{2}$ |
$[\frac{1}{2},\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 9 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.22 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.23 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{2} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.24 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{2} + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{2} + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.25 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[2,\frac{9}{4}]^{2}$ |
$[1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.26 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{2} + 9 x + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[2,\frac{9}{4}]^{2}$ |
$[1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{2} + 9 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.27 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{2} + 9 x + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^2:D_{12}$ (as 12T118) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[2,\frac{9}{4}]^{2}$ |
$[1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{2} + 9 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.28 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 9 x + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 9 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.29 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{2} + 9 x + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 9 x^{2} + 9 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a1.30 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{2} + 9 x + 6$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3^3:D_{12}$ (as 12T169) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$1$ |
$t + 1$ |
$x^{12} + 6 x^{11} + 3 x^{10} + 18 x^{2} + 9 x + 6$ |
$[10, 0]$ |
$[2, 2]$ |
$z^9 + z^6 + 1,z^2 + 1$ |
undefined |
| 3.1.12.21a2.1 |
$12$ |
$x^{12} + 3 x^{10} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$6$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.2 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$6$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ |
$[\frac{9}{4}]^{6}$ |
$[\frac{5}{4}]^{6}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.3 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$6$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.4 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$6$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ |
$[\frac{9}{4}]^{6}$ |
$[\frac{5}{4}]^{6}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.5 |
$12$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{9}{4}]^{2}$ |
$[\frac{5}{4}]^{2}$ |
$6$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.6 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:C_6$ (as 12T121) |
$6$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}, \frac{9}{4}]_{4}^{6}$ |
$[\frac{5}{4},\frac{5}{4}]_{4}^{6}$ |
$[\frac{9}{4}]^{6}$ |
$[\frac{5}{4}]^{6}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.7 |
$12$ |
$x^{12} + 3 x^{10} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},\frac{9}{4}]^{2}$ |
$[\frac{1}{2},\frac{5}{4}]^{2}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.8 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ |
$[\frac{3}{2},\frac{9}{4}]^{6}$ |
$[\frac{1}{2},\frac{5}{4}]^{6}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 9 x + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.9 |
$12$ |
$x^{12} + 3 x^{10} + 18 x^{3} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ |
$[\frac{3}{2},\frac{9}{4}]^{6}$ |
$[\frac{1}{2},\frac{5}{4}]^{6}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 18 x^{3} + 9 x + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.10 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},\frac{9}{4}]^{2}$ |
$[\frac{1}{2},\frac{5}{4}]^{2}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.11 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ |
$[\frac{3}{2},\frac{9}{4}]^{6}$ |
$[\frac{1}{2},\frac{5}{4}]^{6}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.12 |
$12$ |
$x^{12} + 3 x^{10} + 18 x^{3} + 9 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ |
$[\frac{3}{2},\frac{9}{4}]^{6}$ |
$[\frac{1}{2},\frac{5}{4}]^{6}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 18 x^{3} + 9 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.13 |
$12$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$S_3^2:S_3$ (as 12T116) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},\frac{9}{4}]^{2}$ |
$[\frac{1}{2},\frac{5}{4}]^{2}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 18 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.14 |
$12$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ |
$[\frac{3}{2},\frac{9}{4}]^{6}$ |
$[\frac{1}{2},\frac{5}{4}]^{6}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 9 x^{3} + 18 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.15 |
$12$ |
$x^{12} + 3 x^{10} + 18 x^{3} + 18 x^{2} + 9 x + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$6$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, \frac{9}{4}, \frac{9}{4}]_{4}^{6}$ |
$[\frac{1}{2},\frac{5}{4},\frac{5}{4}]_{4}^{6}$ |
$[\frac{3}{2},\frac{9}{4}]^{6}$ |
$[\frac{1}{2},\frac{5}{4}]^{6}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{10} + 18 x^{3} + 18 x^{2} + 9 x + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.16 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.17 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.18 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{2} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.19 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 9 x^{3} + 9 x^{2} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
| 3.1.12.21a2.20 |
$12$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{2} + 3$ |
$3$ |
$1$ |
$12$ |
$21$ |
$C_3\wr D_4$ (as 12T167) |
$2$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{3}{2}, 2, \frac{9}{4}, \frac{9}{4}]_{4}^{2}$ |
$[\frac{1}{2},1,\frac{5}{4},\frac{5}{4}]_{4}^{2}$ |
$[\frac{3}{2},2,\frac{9}{4}]^{2}$ |
$[\frac{1}{2},1,\frac{5}{4}]^{2}$ |
$3$ |
$t + 1$ |
$x^{12} + 3 x^{11} + 3 x^{10} + 18 x^{2} + 3$ |
$[10, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 14]$ |
