| 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 |
| 2.1.12.12a1.1 |
$12$ |
$x^{12} + 2 x + 2$ |
$2$ |
$1$ |
$12$ |
$12$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[\frac{10}{9}, \frac{10}{9}]$ |
$[\frac{1}{9},\frac{1}{9}]$ |
$[\frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}, \frac{10}{9}]_{9}^{6}$ |
$[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9}]_{9}^{6}$ |
$[\frac{10}{9},\frac{10}{9},\frac{10}{9},\frac{10}{9}]^{6}_{3}$ |
$[\frac{1}{9},\frac{1}{9},\frac{1}{9},\frac{1}{9}]^{6}_{3}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x + 2$ |
$[1, 1, 0]$ |
$[2, 1]$ |
$z^8 + z^4 + 1,z + 1$ |
$[3, 6, 13]$ |
| 2.1.12.14a1.1 |
$12$ |
$x^{12} + 2 x^{3} + 2$ |
$2$ |
$1$ |
$12$ |
$14$ |
$S_4$ (as 12T8) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}]$ |
$[\frac{1}{3},\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{3} + 2$ |
$[3, 3, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 6, 15]$ |
| 2.1.12.14a1.2 |
$12$ |
$x^{12} + 2 x^{4} + 2 x^{3} + 2$ |
$2$ |
$1$ |
$12$ |
$14$ |
$A_4:C_4$ (as 12T27) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}]$ |
$[\frac{1}{3},\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{4} + 2 x^{3} + 2$ |
$[3, 3, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 6, 15]$ |
| 2.1.12.14a2.1 |
$12$ |
$x^{12} + 2 x^{3} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$14$ |
$A_4\wr C_2$ (as 12T128) |
$6$ |
$3$ |
$[\frac{4}{3}, \frac{4}{3}]$ |
$[\frac{1}{3},\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3}]^{6}$ |
$[\frac{1}{3},\frac{1}{3}]^{6}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{3} + 2 x^{2} + 2$ |
$[3, 2, 0]$ |
$[2, 3]$ |
$z^8 + z^4 + 1,z^3 + z + 1$ |
$[3, 7, 15]$ |
| 2.1.12.16a1.1 |
$12$ |
$x^{12} + 2 x^{5} + 2$ |
$2$ |
$1$ |
$12$ |
$16$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[\frac{14}{9}, \frac{14}{9}]$ |
$[\frac{5}{9},\frac{5}{9}]$ |
$[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}]_{9}^{6}$ |
$[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]_{9}^{6}$ |
$[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}_{3}$ |
$[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}_{3}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{5} + 2$ |
$[5, 5, 0]$ |
$[2, 1]$ |
$z^8 + z^4 + 1,z + 1$ |
$[3, 6, 17]$ |
| 2.1.12.16a1.2 |
$12$ |
$x^{12} + 2 x^{6} + 2 x^{5} + 2$ |
$2$ |
$1$ |
$12$ |
$16$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[\frac{14}{9}, \frac{14}{9}]$ |
$[\frac{5}{9},\frac{5}{9}]$ |
$[\frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}, \frac{14}{9}]_{9}^{6}$ |
$[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]_{9}^{6}$ |
$[\frac{14}{9},\frac{14}{9},\frac{14}{9},\frac{14}{9}]^{6}_{3}$ |
$[\frac{5}{9},\frac{5}{9},\frac{5}{9},\frac{5}{9}]^{6}_{3}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{6} + 2 x^{5} + 2$ |
$[5, 5, 0]$ |
$[2, 1]$ |
$z^8 + z^4 + 1,z + 1$ |
$[3, 6, 17]$ |
| 2.1.12.16b1.1 |
$12$ |
$x^{12} + 2 x^{8} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$16$ |
$C_4^2:S_3$ (as 12T65) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{5}{3}]$ |
$[\frac{1}{3},\frac{2}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3}]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{8} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 17]$ |
| 2.1.12.16b1.2 |
$12$ |
$x^{12} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$16$ |
$C_2^3.S_4$ (as 12T98) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{5}{3}]$ |
$[\frac{1}{3},\frac{2}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{4}{3},\frac{5}{3}]^{4}$ |
$[\frac{1}{3},\frac{2}{3}]^{4}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 17]$ |
| 2.1.12.16b1.3 |
$12$ |
$x^{12} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$16$ |
$C_2^3.S_4$ (as 12T98) |
$4$ |
$3$ |
$[\frac{4}{3}, \frac{5}{3}]$ |
$[\frac{1}{3},\frac{2}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{4}{3},\frac{5}{3}]^{4}$ |
$[\frac{1}{3},\frac{2}{3}]^{4}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 17]$ |
| 2.1.12.16b1.4 |
$12$ |
$x^{12} + 2 x^{8} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$16$ |
$C_4^2:S_3$ (as 12T64) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{5}{3}]$ |
$[\frac{1}{3},\frac{2}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3}]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{8} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 17]$ |
| 2.1.12.16b1.5 |
$12$ |
$x^{12} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$16$ |
$C_4^2:S_3$ (as 12T63) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{5}{3}]$ |
$[\frac{1}{3},\frac{2}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3}]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 17]$ |
| 2.1.12.16b1.6 |
$12$ |
$x^{12} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$16$ |
$C_4^2:S_3$ (as 12T62) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{5}{3}]$ |
$[\frac{1}{3},\frac{2}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3}]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2$ |
$[5, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 17]$ |
| 2.1.12.18a1.1 |
$12$ |
$x^{12} + 2 x^{7} + 2$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[\frac{16}{9}, \frac{16}{9}]$ |
$[\frac{7}{9},\frac{7}{9}]$ |
$[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}]_{9}^{6}$ |
$[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]_{9}^{6}$ |
$[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}_{3}$ |
$[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}_{3}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{7} + 2$ |
$[7, 7, 0]$ |
$[2, 1]$ |
$z^8 + z^4 + 1,z + 1$ |
$[3, 9, 19]$ |
| 2.1.12.18a1.2 |
$12$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[\frac{16}{9}, \frac{16}{9}]$ |
$[\frac{7}{9},\frac{7}{9}]$ |
$[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}]_{9}^{6}$ |
$[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]_{9}^{6}$ |
$[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}_{3}$ |
$[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}_{3}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2$ |
$[7, 7, 0]$ |
$[2, 1]$ |
$z^8 + z^4 + 1,z + 1$ |
$[3, 9, 19]$ |
| 2.1.12.18a1.3 |
$12$ |
$x^{12} + 2 x^{7} + 2 x^{6} + 2$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[\frac{16}{9}, \frac{16}{9}]$ |
$[\frac{7}{9},\frac{7}{9}]$ |
$[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}]_{9}^{6}$ |
$[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]_{9}^{6}$ |
$[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}_{3}$ |
$[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}_{3}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{7} + 2 x^{6} + 2$ |
$[7, 6, 0]$ |
$[2, 1]$ |
$z^8 + z^4 + 1,z + 1$ |
$[3, 6, 19]$ |
| 2.1.12.18a1.4 |
$12$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2 x^{6} + 2$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2^6:C_9:C_6$ (as 12T254) |
$6$ |
$9$ |
$[\frac{16}{9}, \frac{16}{9}]$ |
$[\frac{7}{9},\frac{7}{9}]$ |
$[\frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}, \frac{16}{9}]_{9}^{6}$ |
$[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]_{9}^{6}$ |
$[\frac{16}{9},\frac{16}{9},\frac{16}{9},\frac{16}{9}]^{6}_{3}$ |
$[\frac{7}{9},\frac{7}{9},\frac{7}{9},\frac{7}{9}]^{6}_{3}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2 x^{6} + 2$ |
$[7, 6, 0]$ |
$[2, 1]$ |
$z^8 + z^4 + 1,z + 1$ |
$[3, 6, 19]$ |
| 2.1.12.18b1.1 |
$12$ |
$x^{12} + 2 x^{7} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_4^2:D_6$ (as 12T97) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3},1]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3},\frac{2}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{7} + 2 x^{2} + 6$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 21]$ |
| 2.1.12.18b1.2 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{7} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2^3.S_4$ (as 12T98) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3},1]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3},\frac{2}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{7} + 2 x^{2} + 2$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 21]$ |
| 2.1.12.18b1.3 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{7} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2^3.S_4$ (as 12T98) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3},1]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3},\frac{2}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{7} + 2 x^{2} + 6$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 21]$ |
| 2.1.12.18b1.4 |
$12$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2 \times S_4$ (as 12T24) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2 x^{2} + 2$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 14]$ |
| 2.1.12.18b1.5 |
$12$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2 \times S_4$ (as 12T24) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2 x^{2} + 6$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 24]$ |
| 2.1.12.18b1.6 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{7} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$12$ |
$18$ |
$A_4:C_4$ (as 12T27) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{7} + 2 x^{2} + 6$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 23]$ |
| 2.1.12.18b1.7 |
$12$ |
$x^{12} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_4^2:D_6$ (as 12T95) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3},1]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3},\frac{2}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 2$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 21]$ |
| 2.1.12.18b1.8 |
$12$ |
$x^{12} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_4^2:D_6$ (as 12T95) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3},1]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3},\frac{2}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 6$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 21]$ |
| 2.1.12.18b1.9 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_4^2:D_6$ (as 12T96) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{5}{3}, \frac{5}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},\frac{2}{3},\frac{2}{3},1]_{3}^{2}$ |
$[\frac{4}{3},\frac{5}{3},\frac{5}{3}]^{2}$ |
$[\frac{1}{3},\frac{2}{3},\frac{2}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 6$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 21]$ |
| 2.1.12.18b1.10 |
$12$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2 \times S_4$ (as 12T22) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{9} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 6$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 23]$ |
| 2.1.12.18b1.11 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2 \times S_4$ (as 12T23) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 2$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 14]$ |
| 2.1.12.18b1.12 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 6$ |
$2$ |
$1$ |
$12$ |
$18$ |
$C_2 \times S_4$ (as 12T23) |
$2$ |
$3$ |
$[\frac{4}{3}, 2]$ |
$[\frac{1}{3},1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1]_{3}^{2}$ |
$[\frac{4}{3}]^{2}$ |
$[\frac{1}{3}]^{2}$ |
$4$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 6$ |
$[7, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 24]$ |
| 2.1.12.20a1.1 |
$12$ |
$x^{12} + 2 x^{9} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[2, 2]_{3}^{2}$ |
$[1,1]_{3}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{9} + 2$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 18]$ |
| 2.1.12.20a1.2 |
$12$ |
$x^{12} + 2 x^{9} + 6$ |
$2$ |
$1$ |
$12$ |
$20$ |
$(C_6\times C_2):C_2$ (as 12T13) |
$2$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[2, 2]_{3}^{2}$ |
$[1,1]_{3}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{9} + 6$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 24]$ |
| 2.1.12.20a1.3 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 23]$ |
| 2.1.12.20a1.4 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 6$ |
$2$ |
$1$ |
$12$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 6$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 23]$ |
| 2.1.12.20a1.5 |
$12$ |
$x^{12} + 2 x^{10} + 2 x^{9} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 2 x^{9} + 2$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 23]$ |
| 2.1.12.20a1.6 |
$12$ |
$x^{12} + 2 x^{10} + 2 x^{9} + 6$ |
$2$ |
$1$ |
$12$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T49) |
$2$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 2 x^{9} + 6$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 23]$ |
| 2.1.12.20a1.7 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T52) |
$2$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 18]$ |
| 2.1.12.20a1.8 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 6$ |
$2$ |
$1$ |
$12$ |
$20$ |
$\GL(2,\mathbb{Z}/4)$ (as 12T52) |
$2$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1]_{3}^{2}$ |
$[\frac{4}{3},\frac{4}{3}]^{2}$ |
$[\frac{1}{3},\frac{1}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 6$ |
$[9, 9, 0]$ |
$[2, 2]$ |
$z^8 + z^4 + 1,z^3 + 1$ |
$[3, 9, 24]$ |
| 2.1.12.20a2.1 |
$12$ |
$x^{12} + 2 x^{9} + 2 x^{6} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$S_3\times A_4$ (as 12T43) |
$6$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[2, 2]_{3}^{6}$ |
$[1,1]_{3}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{9} + 2 x^{6} + 2$ |
$[9, 6, 0]$ |
$[2, 3]$ |
$z^8 + z^4 + 1,z^3 + z + 1$ |
$[3, 6, 21]$ |
| 2.1.12.20a2.2 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{6} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^4:(S_3\times A_4)$ (as 12T206) |
$6$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{6}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{6} + 2$ |
$[9, 6, 0]$ |
$[2, 3]$ |
$z^8 + z^4 + 1,z^3 + z + 1$ |
$[3, 6, 21]$ |
| 2.1.12.20a2.3 |
$12$ |
$x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{6} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^4:(S_3\times A_4)$ (as 12T206) |
$6$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{6}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{10} + 2 x^{9} + 2 x^{6} + 2$ |
$[9, 6, 0]$ |
$[2, 3]$ |
$z^8 + z^4 + 1,z^3 + z + 1$ |
$[3, 6, 21]$ |
| 2.1.12.20a2.4 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{6} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^4:(S_3\times A_4)$ (as 12T206) |
$6$ |
$3$ |
$[2, 2]$ |
$[1,1]$ |
$[\frac{4}{3}, \frac{4}{3}, \frac{4}{3}, \frac{4}{3}, 2, 2]_{3}^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3},1,1]_{3}^{6}$ |
$[\frac{4}{3},\frac{4}{3},\frac{4}{3},\frac{4}{3}]^{6}$ |
$[\frac{1}{3},\frac{1}{3},\frac{1}{3},\frac{1}{3}]^{6}$ |
$1$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{10} + 2 x^{9} + 2 x^{6} + 2$ |
$[9, 6, 0]$ |
$[2, 3]$ |
$z^8 + z^4 + 1,z^3 + z + 1$ |
$[3, 6, 21]$ |
| 2.1.12.20b1.1 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^4:S_4$ (as 12T146) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2 x^{2} + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
| 2.1.12.20b1.2 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^4:S_4$ (as 12T146) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
| 2.1.12.20b1.3 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T149) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
| 2.1.12.20b1.4 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T149) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
| 2.1.12.20b1.5 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^4:S_4$ (as 12T146) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{2} + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
| 2.1.12.20b1.6 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^4:S_4$ (as 12T146) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 2 x^{2} + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
| 2.1.12.20b1.7 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{2} + 4 x + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T149) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
| 2.1.12.20b1.8 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 2 x^{2} + 4 x + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_2^2.\GL(2,\mathbb{Z}/4)$ (as 12T149) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 4 x^{4} + 2 x^{2} + 4 x + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
| 2.1.12.20b1.9 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 6 x^{4} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_4^2:D_6$ (as 12T115) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 6 x^{4} + 2 x^{2} + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
| 2.1.12.20b1.10 |
$12$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$2$ |
$1$ |
$12$ |
$20$ |
$C_4^2:D_6$ (as 12T115) |
$2$ |
$3$ |
$[\frac{4}{3}, \frac{7}{3}]$ |
$[\frac{1}{3},\frac{4}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}, 2, \frac{7}{3}, \frac{7}{3}]_{3}^{2}$ |
$[\frac{1}{3},\frac{1}{3},1,\frac{4}{3},\frac{4}{3}]_{3}^{2}$ |
$[\frac{4}{3},2,\frac{7}{3}]^{2}$ |
$[\frac{1}{3},1,\frac{4}{3}]^{2}$ |
$2$ |
$t + 1$ |
$x^{12} + 2 x^{11} + 2 x^{9} + 2 x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[9, 2, 0]$ |
$[2, 1, 1]$ |
$z^8 + z^4 + 1,z^2 + 1,z + 1$ |
$[3, 7, 19]$ |
