| 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 |
| 5.1.1.0a1.1 |
$1$ |
$x + 3$ |
$5$ |
$1$ |
$1$ |
$0$ |
Trivial (as 1T1) |
$1$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$1$ |
$t + 3$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.2.1.0a1.1 |
$2$ |
$x^{2} + 4 x + 2$ |
$5$ |
$2$ |
$1$ |
$0$ |
$C_2$ (as 2T1) |
$2$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t^{2} + 4 t + 2$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.1.2.1a1.1 |
$2$ |
$x^{2} + 5$ |
$5$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 3$ |
$x^{2} + 5$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.1.2.1a1.2 |
$2$ |
$x^{2} + 10$ |
$5$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 3$ |
$x^{2} + 10$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.3.1.0a1.1 |
$3$ |
$x^{3} + 3 x + 3$ |
$5$ |
$3$ |
$1$ |
$0$ |
$C_3$ (as 3T1) |
$3$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.1.3.2a1.1 |
$3$ |
$x^{3} + 5$ |
$5$ |
$1$ |
$3$ |
$2$ |
$S_3$ (as 3T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 3$ |
$x^{3} + 5$ |
$[0]$ |
$[2]$ |
$z^2 + 3 z + 3$ |
undefined |
| 5.4.1.0a1.1 |
$4$ |
$x^{4} + 4 x^{2} + 4 x + 2$ |
$5$ |
$4$ |
$1$ |
$0$ |
$C_4$ (as 4T1) |
$4$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{4} + 4 t^{2} + 4 t + 2$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.2.2.2a1.1 |
$4$ |
$( x^{2} + 4 x + 2 )^{2} + 5 x$ |
$5$ |
$2$ |
$2$ |
$2$ |
$C_4$ (as 4T1) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{2} + 5 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.2.2.2a1.2 |
$4$ |
$( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{2} + 5$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.1.4.3a1.1 |
$4$ |
$x^{4} + 5$ |
$5$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 3$ |
$x^{4} + 5$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + z + 4$ |
$[1]$ |
| 5.1.4.3a1.2 |
$4$ |
$x^{4} + 10$ |
$5$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 3$ |
$x^{4} + 10$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + z + 4$ |
undefined |
| 5.1.4.3a1.3 |
$4$ |
$x^{4} + 15$ |
$5$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 3$ |
$x^{4} + 15$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + z + 4$ |
undefined |
| 5.1.4.3a1.4 |
$4$ |
$x^{4} + 20$ |
$5$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 3$ |
$x^{4} + 20$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + z + 4$ |
undefined |
| 5.5.1.0a1.1 |
$5$ |
$x^{5} + 4 x + 3$ |
$5$ |
$5$ |
$1$ |
$0$ |
$C_5$ (as 5T1) |
$5$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t^{5} + 4 t + 3$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.1.5.5a1.1 |
$5$ |
$x^{5} + 5 x + 5$ |
$5$ |
$1$ |
$5$ |
$5$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 5 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.5a1.2 |
$5$ |
$x^{5} + 10 x + 5$ |
$5$ |
$1$ |
$5$ |
$5$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 10 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.5a1.3 |
$5$ |
$x^{5} + 15 x + 5$ |
$5$ |
$1$ |
$5$ |
$5$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 15 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.5a1.4 |
$5$ |
$x^{5} + 20 x + 5$ |
$5$ |
$1$ |
$5$ |
$5$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}]_{4}$ |
$[\frac{1}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 20 x + 5$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.6a1.1 |
$5$ |
$x^{5} + 10 x^{2} + 5$ |
$5$ |
$1$ |
$5$ |
$6$ |
$D_{5}$ (as 5T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$1$ |
$t + 3$ |
$x^{5} + 10 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 1$ |
undefined |
| 5.1.5.6a1.2 |
$5$ |
$x^{5} + 15 x^{2} + 5$ |
$5$ |
$1$ |
$5$ |
$6$ |
$D_{5}$ (as 5T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$1$ |
$t + 3$ |
$x^{5} + 15 x^{2} + 5$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 1$ |
undefined |
| 5.1.5.6a2.1 |
$5$ |
$x^{5} + 5 x^{2} + 5$ |
$5$ |
$1$ |
$5$ |
$6$ |
$F_5$ (as 5T3) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{5} + 5 x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + 2$ |
undefined |
| 5.1.5.6a2.2 |
$5$ |
$x^{5} + 20 x^{2} + 5$ |
$5$ |
$1$ |
$5$ |
$6$ |
$F_5$ (as 5T3) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{5} + 20 x^{2} + 5$ |
$[2, 0]$ |
$[2]$ |
$z^2 + 2$ |
undefined |
| 5.1.5.7a1.1 |
$5$ |
$x^{5} + 5 x^{3} + 5$ |
$5$ |
$1$ |
$5$ |
$7$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 5 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.7a1.2 |
$5$ |
$x^{5} + 10 x^{3} + 5$ |
$5$ |
$1$ |
$5$ |
$7$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 10 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.7a1.3 |
$5$ |
$x^{5} + 15 x^{3} + 5$ |
$5$ |
$1$ |
$5$ |
$7$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 15 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.7a1.4 |
$5$ |
$x^{5} + 20 x^{3} + 5$ |
$5$ |
$1$ |
$5$ |
$7$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
$[\frac{7}{4}]_{4}$ |
$[\frac{3}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 20 x^{3} + 5$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.8a1.1 |
$5$ |
$x^{5} + 5 x^{4} + 5$ |
$5$ |
$1$ |
$5$ |
$8$ |
$D_{5}$ (as 5T2) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 3$ |
$x^{5} + 5 x^{4} + 5$ |
$[4, 0]$ |
$[2]$ |
$z^4 + 1$ |
undefined |
| 5.1.5.8a2.1 |
$5$ |
$x^{5} + 10 x^{4} + 5$ |
$5$ |
$1$ |
$5$ |
$8$ |
$F_5$ (as 5T3) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{4}$ |
$[1]^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 10 x^{4} + 5$ |
$[4, 0]$ |
$[4]$ |
$z^4 + 2$ |
undefined |
| 5.1.5.8a3.1 |
$5$ |
$x^{5} + 15 x^{4} + 5$ |
$5$ |
$1$ |
$5$ |
$8$ |
$F_5$ (as 5T3) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{4}$ |
$[1]^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 15 x^{4} + 5$ |
$[4, 0]$ |
$[4]$ |
$z^4 + 3$ |
undefined |
| 5.1.5.8a4.1 |
$5$ |
$x^{5} + 20 x^{4} + 5$ |
$5$ |
$1$ |
$5$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 5$ |
$[4, 0]$ |
$[1]$ |
$z^4 + 4$ |
undefined |
| 5.1.5.8a4.2 |
$5$ |
$x^{5} + 20 x^{4} + 30$ |
$5$ |
$1$ |
$5$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 30$ |
$[4, 0]$ |
$[1]$ |
$z^4 + 4$ |
undefined |
| 5.1.5.8a4.3 |
$5$ |
$x^{5} + 20 x^{4} + 55$ |
$5$ |
$1$ |
$5$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 55$ |
$[4, 0]$ |
$[1]$ |
$z^4 + 4$ |
undefined |
| 5.1.5.8a4.4 |
$5$ |
$x^{5} + 20 x^{4} + 80$ |
$5$ |
$1$ |
$5$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 80$ |
$[4, 0]$ |
$[1]$ |
$z^4 + 4$ |
undefined |
| 5.1.5.8a4.5 |
$5$ |
$x^{5} + 20 x^{4} + 105$ |
$5$ |
$1$ |
$5$ |
$8$ |
$C_5$ (as 5T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 3$ |
$x^{5} + 20 x^{4} + 105$ |
$[4, 0]$ |
$[1]$ |
$z^4 + 4$ |
undefined |
| 5.1.5.9a1.1 |
$5$ |
$x^{5} + 5$ |
$5$ |
$1$ |
$5$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}]_{4}$ |
$[\frac{5}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 5$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.9a1.2 |
$5$ |
$x^{5} + 25 x + 5$ |
$5$ |
$1$ |
$5$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}]_{4}$ |
$[\frac{5}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 25 x + 5$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.9a1.3 |
$5$ |
$x^{5} + 50 x + 5$ |
$5$ |
$1$ |
$5$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}]_{4}$ |
$[\frac{5}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 50 x + 5$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.9a1.4 |
$5$ |
$x^{5} + 75 x + 5$ |
$5$ |
$1$ |
$5$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}]_{4}$ |
$[\frac{5}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 75 x + 5$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.1.5.9a1.5 |
$5$ |
$x^{5} + 100 x + 5$ |
$5$ |
$1$ |
$5$ |
$9$ |
$F_5$ (as 5T3) |
$1$ |
$4$ |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
$[\frac{9}{4}]_{4}$ |
$[\frac{5}{4}]_{4}$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$1$ |
$t + 3$ |
$x^{5} + 100 x + 5$ |
$[5, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 5.6.1.0a1.1 |
$6$ |
$x^{6} + x^{4} + 4 x^{3} + x^{2} + 2$ |
$5$ |
$6$ |
$1$ |
$0$ |
$C_6$ (as 6T1) |
$6$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{6} + t^{4} + 4 t^{3} + t^{2} + 2$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.3.2.3a1.1 |
$6$ |
$( x^{3} + 3 x + 3 )^{2} + 5 x$ |
$5$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + 3 t + 3$ |
$x^{2} + 5 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.3.2.3a1.2 |
$6$ |
$( x^{3} + 3 x + 3 )^{2} + 5$ |
$5$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + 3 t + 3$ |
$x^{2} + 5$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 5.2.3.4a1.1 |
$6$ |
$( x^{2} + 4 x + 2 )^{3} + 5 x$ |
$5$ |
$2$ |
$3$ |
$4$ |
$S_3\times C_3$ (as 6T5) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$3$ |
$t^{2} + 4 t + 2$ |
$x^{3} + 5 t + 15$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 5.2.3.4a1.2 |
$6$ |
$( x^{2} + 4 x + 2 )^{3} + 5$ |
$5$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 4 t + 2$ |
$x^{3} + 5$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 5.1.6.5a1.1 |
$6$ |
$x^{6} + 5$ |
$5$ |
$1$ |
$6$ |
$5$ |
$D_{6}$ (as 6T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[\ ]_{6}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 3$ |
$x^{6} + 5$ |
$[0]$ |
$[2]$ |
$z^5 + z^4 + 1$ |
undefined |
| 5.1.6.5a1.2 |
$6$ |
$x^{6} + 10$ |
$5$ |
$1$ |
$6$ |
$5$ |
$D_{6}$ (as 6T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[\ ]_{6}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 3$ |
$x^{6} + 10$ |
$[0]$ |
$[2]$ |
$z^5 + z^4 + 1$ |
undefined |
| 5.7.1.0a1.1 |
$7$ |
$x^{7} + 3 x + 3$ |
$5$ |
$7$ |
$1$ |
$0$ |
$C_7$ (as 7T1) |
$7$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{7}$ |
$[\ ]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t^{7} + 3 t + 3$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.1.7.6a1.1 |
$7$ |
$x^{7} + 5$ |
$5$ |
$1$ |
$7$ |
$6$ |
$F_7$ (as 7T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 3$ |
$x^{7} + 5$ |
$[0]$ |
$[6]$ |
$z^6 + 2 z^5 + z^4 + z + 2$ |
undefined |
| 5.8.1.0a1.1 |
$8$ |
$x^{8} + x^{4} + 3 x^{2} + 4 x + 2$ |
$5$ |
$8$ |
$1$ |
$0$ |
$C_8$ (as 8T1) |
$8$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{8}$ |
$[\ ]^{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{8} + t^{4} + 3 t^{2} + 4 t + 2$ |
$x - 5$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 5.4.2.4a1.1 |
$8$ |
$( x^{4} + 4 x^{2} + 4 x + 2 )^{2} + 5 x$ |
$5$ |
$4$ |
$2$ |
$4$ |
$C_8$ (as 8T1) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 4 t^{2} + 4 t + 2$ |
$x^{2} + 5 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
