| 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 |
| 2.6.2.12a5.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{3} + 2 x^{2} + 2 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{6}$ |
$[1,1]^{6}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2 t\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^2 + t)$ |
$[1, 3]$ |
| 2.6.2.12a5.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{3} + 2 x^{2} + 2 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 6$ |
$2$ |
$6$ |
$2$ |
$12$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{6}$ |
$[1,1]^{6}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^2 + t)$ |
$[1, 3]$ |
| 2.6.2.18a1.15 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 3]^{6}$ |
$[1,2]^{6}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.16 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 3]^{6}$ |
$[1,2]^{6}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.3.4.18a1.1 |
$12$ |
$( x^{3} + x + 1 )^{4} + 2 ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$4$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2, 2]$ |
$[1,1]$ |
$[2, 2]^{6}$ |
$[1,1]^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + 2$ |
$[3, 3, 0]$ |
$[2]$ |
$z^3 + (t^2 + t)$ |
$[1, 3, 6]$ |
| 2.3.4.18a1.2 |
$12$ |
$( x^{3} + x + 1 )^{4} + 2 ( x^{3} + x + 1 )^{3} + 6$ |
$2$ |
$3$ |
$4$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2, 2]$ |
$[1,1]$ |
$[2, 2]^{6}$ |
$[1,1]^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + 6$ |
$[3, 3, 0]$ |
$[2]$ |
$z^3 + (t^2 + t)$ |
$[1, 3, 8]$ |
| 2.3.4.24b1.5 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 2 ( x^{3} + x + 1 )^{2} + 4 ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$4$ |
$24$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]^{6}$ |
$[1,2]^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t^2$ |
$[1, 7, 11]$ |
| 2.3.4.24b1.7 |
$12$ |
$( x^{3} + x + 1 )^{4} + 2 ( x^{3} + x + 1 )^{2} + 4 ( x^{3} + x + 1 ) + 6$ |
$2$ |
$3$ |
$4$ |
$24$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]^{6}$ |
$[1,2]^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t^2$ |
$[1, 2, 8]$ |
| 2.3.4.27a1.1 |
$12$ |
$( x^{3} + x + 1 )^{4} + 2 ( x^{3} + x + 1 )^{2} + 2$ |
$2$ |
$3$ |
$4$ |
$27$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[3]$ |
$[2]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t$ |
$[1, 5, 9]$ |
| 2.3.4.27a1.2 |
$12$ |
$( x^{3} + x + 1 )^{4} + 10 ( x^{3} + x + 1 )^{2} + 2$ |
$2$ |
$3$ |
$4$ |
$27$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[3]$ |
$[2]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 10 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t$ |
$[1, 5, 9]$ |
| 2.3.4.27a1.13 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 2 ( x^{3} + x + 1 )^{2} + 2$ |
$2$ |
$3$ |
$4$ |
$27$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[3]$ |
$[2]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t$ |
$[1, 5, 9]$ |
| 2.3.4.27a1.14 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 10 ( x^{3} + x + 1 )^{2} + 2$ |
$2$ |
$3$ |
$4$ |
$27$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[3]$ |
$[2]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 10 x^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t$ |
$[1, 5, 9]$ |
| 2.3.4.27a1.25 |
$12$ |
$( x^{3} + x + 1 )^{4} + 2 ( x^{3} + x + 1 )^{2} + 6$ |
$2$ |
$3$ |
$4$ |
$27$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[3]$ |
$[2]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t$ |
$[1, 2, 8]$ |
| 2.3.4.27a1.26 |
$12$ |
$( x^{3} + x + 1 )^{4} + 10 ( x^{3} + x + 1 )^{2} + 6$ |
$2$ |
$3$ |
$4$ |
$27$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[3]$ |
$[2]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 10 x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t$ |
$[1, 2, 8]$ |
| 2.3.4.27a1.29 |
$12$ |
$( x^{3} + x + 1 )^{4} + 2 ( x^{3} + x + 1 )^{2} + 8 ( x^{3} + x + 1 ) + 6$ |
$2$ |
$3$ |
$4$ |
$27$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[3]$ |
$[2]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{2} + 8 x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t$ |
$[1, 2, 8]$ |
| 2.3.4.27a1.39 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 2 ( x^{3} + x + 1 )^{2} + 8 ( x^{3} + x + 1 ) + 6$ |
$2$ |
$3$ |
$4$ |
$27$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[3]$ |
$[2]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 8 x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^2 + t + 1),(t^2 + t + 1) z + t$ |
$[1, 2, 8]$ |
| 2.3.4.30a1.1 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 2$ |
$2$ |
$3$ |
$4$ |
$30$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + 1$ |
$[1, 3, 7]$ |
| 2.3.4.30a1.2 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 8 ( x^{3} + x + 1 )^{2} + 2$ |
$2$ |
$3$ |
$4$ |
$30$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 8 x^{2} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + 1$ |
$[1, 3, 7]$ |
| 2.3.4.30a1.5 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 10$ |
$2$ |
$3$ |
$4$ |
$30$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + 1$ |
$[1, 3, 7]$ |
| 2.3.4.30a1.6 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 8 ( x^{3} + x + 1 )^{2} + 10$ |
$2$ |
$3$ |
$4$ |
$30$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 8 x^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + 1$ |
$[1, 3, 7]$ |
| 2.3.4.30a1.25 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 4 ( x^{3} + x + 1 )^{2} + 2$ |
$2$ |
$3$ |
$4$ |
$30$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 4 x^{2} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + 1$ |
$[1, 3, 7]$ |
| 2.3.4.30a1.26 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 12 ( x^{3} + x + 1 )^{2} + 2$ |
$2$ |
$3$ |
$4$ |
$30$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 12 x^{2} + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + 1$ |
$[1, 3, 7]$ |
| 2.3.4.30a1.29 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 4 ( x^{3} + x + 1 )^{2} + 10$ |
$2$ |
$3$ |
$4$ |
$30$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 4 x^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + 1$ |
$[1, 3, 7]$ |
| 2.3.4.30a1.30 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{3} + 12 ( x^{3} + x + 1 )^{2} + 10$ |
$2$ |
$3$ |
$4$ |
$30$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 3, \frac{7}{2}]^{3}$ |
$[1,2,\frac{5}{2}]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 12 x^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + 1$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.1 |
$12$ |
$( x^{3} + x + 1 )^{4} + 2$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{3}$ |
$[1,2,3]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.2 |
$12$ |
$( x^{3} + x + 1 )^{4} + 18$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{3}$ |
$[1,2,3]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.13 |
$12$ |
$( x^{3} + x + 1 )^{4} + 8 ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{6}$ |
$[2,3]^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.15 |
$12$ |
$( x^{3} + x + 1 )^{4} + 8 ( x^{3} + x + 1 )^{3} + 8 ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{6}$ |
$[2,3]^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.25 |
$12$ |
$( x^{3} + x + 1 )^{4} + 10$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{3}$ |
$[1,2,3]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.26 |
$12$ |
$( x^{3} + x + 1 )^{4} + 26$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{3}$ |
$[1,2,3]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.37 |
$12$ |
$( x^{3} + x + 1 )^{4} + 8 ( x^{3} + x + 1 ) + 10$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{6}$ |
$[2,3]^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.39 |
$12$ |
$( x^{3} + x + 1 )^{4} + 8 ( x^{3} + x + 1 )^{3} + 8 ( x^{3} + x + 1 ) + 10$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{6}$ |
$[2,3]^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.193 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{2} + 8 ( x^{3} + x + 1 ) + 2$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{3}$ |
$[1,2,3]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.194 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{2} + 8 ( x^{3} + x + 1 ) + 18$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{3}$ |
$[1,2,3]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{2} + 8 x + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.221 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{2} + 8 ( x^{3} + x + 1 ) + 10$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{3}$ |
$[1,2,3]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{2} + 8 x + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 2.3.4.33a1.222 |
$12$ |
$( x^{3} + x + 1 )^{4} + 4 ( x^{3} + x + 1 )^{2} + 8 ( x^{3} + x + 1 ) + 26$ |
$2$ |
$3$ |
$4$ |
$33$ |
$D_4 \times C_3$ (as 12T14) |
$3$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{3}$ |
$[1,2,3]^{3}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{2} + 8 x + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + (t + 1),(t + 1) z + (t^2 + 1)$ |
$[1, 3, 7]$ |
| 3.3.4.9a1.1 |
$12$ |
$( x^{3} + 2 x + 1 )^{4} + 3 x$ |
$3$ |
$3$ |
$4$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$[\ ]_{4}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{4} + 3 t$ |
$[0]$ |
$[2]$ |
$z^3 + z^2 + 1$ |
undefined |
| 3.3.4.9a1.2 |
$12$ |
$( x^{3} + 2 x + 1 )^{4} + 3$ |
$3$ |
$3$ |
$4$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$[\ ]_{4}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{4} + 3$ |
$[0]$ |
$[2]$ |
$z^3 + z^2 + 1$ |
$[2]$ |
| 3.1.12.19a2.1 |
$12$ |
$x^{12} + 6 x^{8} + 3$ |
$3$ |
$1$ |
$12$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[1]$ |
$[2]_{4}^{2}$ |
$[1]_{4}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 1$ |
$x^{12} + 6 x^{8} + 3$ |
$[8, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 6]$ |
| 3.1.12.19a2.2 |
$12$ |
$x^{12} + 6 x^{8} + 12$ |
$3$ |
$1$ |
$12$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[1]$ |
$[2]_{4}^{2}$ |
$[1]_{4}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 1$ |
$x^{12} + 6 x^{8} + 12$ |
$[8, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 18]$ |
| 3.1.12.19a2.3 |
$12$ |
$x^{12} + 6 x^{8} + 21$ |
$3$ |
$1$ |
$12$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[1]$ |
$[2]_{4}^{2}$ |
$[1]_{4}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 1$ |
$x^{12} + 6 x^{8} + 21$ |
$[8, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
$[2, 18]$ |
| 3.1.12.19a2.19 |
$12$ |
$x^{12} + 3 x^{8} + 6$ |
$3$ |
$1$ |
$12$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[1]$ |
$[2]_{4}^{2}$ |
$[1]_{4}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 1$ |
$x^{12} + 3 x^{8} + 6$ |
$[8, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
undefined |
| 3.1.12.19a2.20 |
$12$ |
$x^{12} + 3 x^{8} + 15$ |
$3$ |
$1$ |
$12$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[1]$ |
$[2]_{4}^{2}$ |
$[1]_{4}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 1$ |
$x^{12} + 3 x^{8} + 15$ |
$[8, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
undefined |
| 3.1.12.19a2.21 |
$12$ |
$x^{12} + 3 x^{8} + 24$ |
$3$ |
$1$ |
$12$ |
$19$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$4$ |
$[2]$ |
$[1]$ |
$[2]_{4}^{2}$ |
$[1]_{4}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 1$ |
$x^{12} + 3 x^{8} + 24$ |
$[8, 0]$ |
$[2, 1]$ |
$z^9 + z^6 + 1,z^2 + 2$ |
undefined |
| 7.3.4.9a1.1 |
$12$ |
$( x^{3} + 6 x^{2} + 4 )^{4} + 7 x$ |
$7$ |
$3$ |
$4$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$[\ ]_{4}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{4} + 7 t$ |
$[0]$ |
$[2]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.3.4.9a1.2 |
$12$ |
$( x^{3} + 6 x^{2} + 4 )^{4} + 7$ |
$7$ |
$3$ |
$4$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$[\ ]_{4}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{4} + 7$ |
$[0]$ |
$[2]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.1.12.11a1.1 |
$12$ |
$x^{12} + 7$ |
$7$ |
$1$ |
$12$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[\ ]_{12}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 4$ |
$x^{12} + 7$ |
$[0]$ |
$[2]$ |
$z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ |
$[2]$ |
| 7.1.12.11a1.2 |
$12$ |
$x^{12} + 14$ |
$7$ |
$1$ |
$12$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[\ ]_{12}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 4$ |
$x^{12} + 14$ |
$[0]$ |
$[2]$ |
$z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ |
undefined |
| 7.1.12.11a1.3 |
$12$ |
$x^{12} + 21$ |
$7$ |
$1$ |
$12$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[\ ]_{12}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 4$ |
$x^{12} + 21$ |
$[0]$ |
$[2]$ |
$z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ |
undefined |
| 7.1.12.11a1.4 |
$12$ |
$x^{12} + 28$ |
$7$ |
$1$ |
$12$ |
$11$ |
$D_4 \times C_3$ (as 12T14) |
$2$ |
$12$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{12}^{2}$ |
$[\ ]_{12}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$6$ |
$t + 4$ |
$x^{12} + 28$ |
$[0]$ |
$[2]$ |
$z^{11} + 5 z^{10} + 3 z^9 + 3 z^8 + 5 z^7 + z^6 + z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ |
undefined |
