| 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 |
| 17.1.1.0a1.1 |
$1$ |
$x + 14$ |
$17$ |
$1$ |
$1$ |
$0$ |
Trivial (as 1T1) |
$1$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$1$ |
$t + 14$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.2.1.0a1.1 |
$2$ |
$x^{2} + 16 x + 3$ |
$17$ |
$2$ |
$1$ |
$0$ |
$C_2$ (as 2T1) |
$2$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t^{2} + 16 t + 3$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.1.2.1a1.1 |
$2$ |
$x^{2} + 17$ |
$17$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 14$ |
$x^{2} + 17$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.1.2.1a1.2 |
$2$ |
$x^{2} + 51$ |
$17$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 14$ |
$x^{2} + 51$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.3.1.0a1.1 |
$3$ |
$x^{3} + x + 14$ |
$17$ |
$3$ |
$1$ |
$0$ |
$C_3$ (as 3T1) |
$3$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t^{3} + t + 14$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.1.3.2a1.1 |
$3$ |
$x^{3} + 17$ |
$17$ |
$1$ |
$3$ |
$2$ |
$S_3$ (as 3T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 14$ |
$x^{3} + 17$ |
$[0]$ |
$[2]$ |
$z^2 + 3 z + 3$ |
undefined |
| 17.4.1.0a1.1 |
$4$ |
$x^{4} + 7 x^{2} + 10 x + 3$ |
$17$ |
$4$ |
$1$ |
$0$ |
$C_4$ (as 4T1) |
$4$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{4} + 7 t^{2} + 10 t + 3$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.2.2.2a1.1 |
$4$ |
$( x^{2} + 16 x + 3 )^{2} + 17 x$ |
$17$ |
$2$ |
$2$ |
$2$ |
$C_4$ (as 4T1) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 16 t + 3$ |
$x^{2} + 17 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.2.2.2a1.2 |
$4$ |
$( x^{2} + 16 x + 3 )^{2} + 17$ |
$17$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 16 t + 3$ |
$x^{2} + 17$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.1.4.3a1.1 |
$4$ |
$x^{4} + 17$ |
$17$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 14$ |
$x^{4} + 17$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.1.4.3a1.2 |
$4$ |
$x^{4} + 51$ |
$17$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 14$ |
$x^{4} + 51$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.1.4.3a1.3 |
$4$ |
$x^{4} + 153$ |
$17$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 14$ |
$x^{4} + 153$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.1.4.3a1.4 |
$4$ |
$x^{4} + 170$ |
$17$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 14$ |
$x^{4} + 170$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.5.1.0a1.1 |
$5$ |
$x^{5} + x + 14$ |
$17$ |
$5$ |
$1$ |
$0$ |
$C_5$ (as 5T1) |
$5$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t^{5} + t + 14$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.1.5.4a1.1 |
$5$ |
$x^{5} + 17$ |
$17$ |
$1$ |
$5$ |
$4$ |
$F_5$ (as 5T3) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$[\ ]_{5}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$1$ |
$t + 14$ |
$x^{5} + 17$ |
$[0]$ |
$[4]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 17.6.1.0a1.1 |
$6$ |
$x^{6} + 2 x^{4} + 10 x^{2} + 3 x + 3$ |
$17$ |
$6$ |
$1$ |
$0$ |
$C_6$ (as 6T1) |
$6$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{6} + 2 t^{4} + 10 t^{2} + 3 t + 3$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.3.2.3a1.1 |
$6$ |
$( x^{3} + x + 14 )^{2} + 17 x$ |
$17$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + t + 14$ |
$x^{2} + 17 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.3.2.3a1.2 |
$6$ |
$( x^{3} + x + 14 )^{2} + 17$ |
$17$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + t + 14$ |
$x^{2} + 17$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.2.3.4a1.1 |
$6$ |
$( x^{2} + 16 x + 3 )^{3} + 17 x$ |
$17$ |
$2$ |
$3$ |
$4$ |
$S_3\times C_3$ (as 6T5) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$3$ |
$t^{2} + 16 t + 3$ |
$x^{3} + 17 t + 238$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 17.2.3.4a1.2 |
$6$ |
$( x^{2} + 16 x + 3 )^{3} + 17$ |
$17$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 16 t + 3$ |
$x^{3} + 17$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 17.1.6.5a1.1 |
$6$ |
$x^{6} + 17$ |
$17$ |
$1$ |
$6$ |
$5$ |
$D_{6}$ (as 6T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[\ ]_{6}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 14$ |
$x^{6} + 17$ |
$[0]$ |
$[2]$ |
$z^5 + 6 z^4 + 15 z^3 + 3 z^2 + 15 z + 6$ |
undefined |
| 17.1.6.5a1.2 |
$6$ |
$x^{6} + 51$ |
$17$ |
$1$ |
$6$ |
$5$ |
$D_{6}$ (as 6T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[\ ]_{6}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 14$ |
$x^{6} + 51$ |
$[0]$ |
$[2]$ |
$z^5 + 6 z^4 + 15 z^3 + 3 z^2 + 15 z + 6$ |
undefined |
| 17.7.1.0a1.1 |
$7$ |
$x^{7} + 12 x + 14$ |
$17$ |
$7$ |
$1$ |
$0$ |
$C_7$ (as 7T1) |
$7$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{7}$ |
$[\ ]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t^{7} + 12 t + 14$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.1.7.6a1.1 |
$7$ |
$x^{7} + 17$ |
$17$ |
$1$ |
$7$ |
$6$ |
$F_7$ (as 7T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 14$ |
$x^{7} + 17$ |
$[0]$ |
$[6]$ |
$z^6 + 7 z^5 + 4 z^4 + z^3 + z^2 + 4 z + 7$ |
undefined |
| 17.8.1.0a1.1 |
$8$ |
$x^{8} + 11 x^{4} + 12 x^{3} + 6 x + 3$ |
$17$ |
$8$ |
$1$ |
$0$ |
$C_8$ (as 8T1) |
$8$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{8}$ |
$[\ ]^{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{8} + 11 t^{4} + 12 t^{3} + 6 t + 3$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.4.2.4a1.1 |
$8$ |
$( x^{4} + 7 x^{2} + 10 x + 3 )^{2} + 17 x$ |
$17$ |
$4$ |
$2$ |
$4$ |
$C_8$ (as 8T1) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 7 t^{2} + 10 t + 3$ |
$x^{2} + 17 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.4.2.4a1.2 |
$8$ |
$( x^{4} + 7 x^{2} + 10 x + 3 )^{2} + 17$ |
$17$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 7 t^{2} + 10 t + 3$ |
$x^{2} + 17$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.2.4.6a1.1 |
$8$ |
$( x^{2} + 16 x + 3 )^{4} + 17 x$ |
$17$ |
$2$ |
$4$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17 t$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.2.4.6a1.2 |
$8$ |
$( x^{2} + 16 x + 3 )^{4} + 17$ |
$17$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.2.4.6a1.3 |
$8$ |
$( x^{2} + 16 x + 3 )^{4} + 17 x + 238$ |
$17$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 17 t + 238$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.2.4.6a1.4 |
$8$ |
$( x^{2} + 16 x + 3 )^{4} + 255 x + 238$ |
$17$ |
$2$ |
$4$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 16 t + 3$ |
$x^{4} + 255 t + 238$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 17.1.8.7a1.1 |
$8$ |
$x^{8} + 17$ |
$17$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 14$ |
$x^{8} + 17$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 11 z^5 + 5 z^4 + 2 z^3 + 5 z^2 + 11 z + 8$ |
undefined |
| 17.1.8.7a1.2 |
$8$ |
$x^{8} + 51$ |
$17$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 14$ |
$x^{8} + 51$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 11 z^5 + 5 z^4 + 2 z^3 + 5 z^2 + 11 z + 8$ |
undefined |
| 17.1.8.7a1.3 |
$8$ |
$x^{8} + 85$ |
$17$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 14$ |
$x^{8} + 85$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 11 z^5 + 5 z^4 + 2 z^3 + 5 z^2 + 11 z + 8$ |
undefined |
| 17.1.8.7a1.4 |
$8$ |
$x^{8} + 153$ |
$17$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 14$ |
$x^{8} + 153$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 11 z^5 + 5 z^4 + 2 z^3 + 5 z^2 + 11 z + 8$ |
undefined |
| 17.1.8.7a1.5 |
$8$ |
$x^{8} + 170$ |
$17$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 14$ |
$x^{8} + 170$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 11 z^5 + 5 z^4 + 2 z^3 + 5 z^2 + 11 z + 8$ |
undefined |
| 17.1.8.7a1.6 |
$8$ |
$x^{8} + 187$ |
$17$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 14$ |
$x^{8} + 187$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 11 z^5 + 5 z^4 + 2 z^3 + 5 z^2 + 11 z + 8$ |
undefined |
| 17.1.8.7a1.7 |
$8$ |
$x^{8} + 221$ |
$17$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 14$ |
$x^{8} + 221$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 11 z^5 + 5 z^4 + 2 z^3 + 5 z^2 + 11 z + 8$ |
undefined |
| 17.1.8.7a1.8 |
$8$ |
$x^{8} + 255$ |
$17$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 14$ |
$x^{8} + 255$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 11 z^5 + 5 z^4 + 2 z^3 + 5 z^2 + 11 z + 8$ |
undefined |
| 17.9.1.0a1.1 |
$9$ |
$x^{9} + 7 x^{2} + 8 x + 14$ |
$17$ |
$9$ |
$1$ |
$0$ |
$C_9$ (as 9T1) |
$9$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{9}$ |
$[\ ]^{9}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{9} + 7 t^{2} + 8 t + 14$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.3.3.6a1.1 |
$9$ |
$( x^{3} + x + 14 )^{3} + 17$ |
$17$ |
$3$ |
$3$ |
$6$ |
$S_3\times C_3$ (as 9T4) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + t + 14$ |
$x^{3} + 17$ |
$[0]$ |
$[2]$ |
$z^2 + 3 z + 3$ |
undefined |
| 17.1.9.8a1.1 |
$9$ |
$x^{9} + 17$ |
$17$ |
$1$ |
$9$ |
$8$ |
$D_{9}$ (as 9T3) |
$2$ |
$9$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{9}^{2}$ |
$[\ ]_{9}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 14$ |
$x^{9} + 17$ |
$[0]$ |
$[2]$ |
$z^8 + 9 z^7 + 2 z^6 + 16 z^5 + 7 z^4 + 7 z^3 + 16 z^2 + 2 z + 9$ |
undefined |
| 17.10.1.0a1.1 |
$10$ |
$x^{10} + 13 x^{5} + 6 x^{4} + 5 x^{3} + 9 x^{2} + 12 x + 3$ |
$17$ |
$10$ |
$1$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{10}$ |
$[\ ]^{10}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{10} + 13 t^{5} + 6 t^{4} + 5 t^{3} + 9 t^{2} + 12 t + 3$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.5.2.5a1.1 |
$10$ |
$( x^{5} + x + 14 )^{2} + 17 x$ |
$17$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t + 14$ |
$x^{2} + 17 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.5.2.5a1.2 |
$10$ |
$( x^{5} + x + 14 )^{2} + 17$ |
$17$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t + 14$ |
$x^{2} + 17$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 17.2.5.8a1.1 |
$10$ |
$( x^{2} + 16 x + 3 )^{5} + 17$ |
$17$ |
$2$ |
$5$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$[\ ]_{5}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t^{2} + 16 t + 3$ |
$x^{5} + 17$ |
$[0]$ |
$[2]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 17.1.10.9a1.1 |
$10$ |
$x^{10} + 17$ |
$17$ |
$1$ |
$10$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$2$ |
$t + 14$ |
$x^{10} + 17$ |
$[0]$ |
$[4]$ |
$z^9 + 10 z^8 + 11 z^7 + z^6 + 6 z^5 + 14 z^4 + 6 z^3 + z^2 + 11 z + 10$ |
undefined |
| 17.1.10.9a1.2 |
$10$ |
$x^{10} + 51$ |
$17$ |
$1$ |
$10$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$2$ |
$t + 14$ |
$x^{10} + 51$ |
$[0]$ |
$[4]$ |
$z^9 + 10 z^8 + 11 z^7 + z^6 + 6 z^5 + 14 z^4 + 6 z^3 + z^2 + 11 z + 10$ |
undefined |
| 17.11.1.0a1.1 |
$11$ |
$x^{11} + 5 x + 14$ |
$17$ |
$11$ |
$1$ |
$0$ |
$C_{11}$ (as 11T1) |
$11$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{11}$ |
$[\ ]^{11}$ |
$[\ ]$ |
$[\ ]$ |
$11$ |
$t^{11} + 5 t + 14$ |
$x - 17$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 17.1.11.10a1.1 |
$11$ |
$x^{11} + 17$ |
$17$ |
$1$ |
$11$ |
$10$ |
$F_{11}$ (as 11T4) |
$10$ |
$11$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{11}^{10}$ |
$[\ ]_{11}^{10}$ |
$[\ ]^{10}$ |
$[\ ]^{10}$ |
$1$ |
$t + 14$ |
$x^{11} + 17$ |
$[0]$ |
$[10]$ |
$z^{10} + 11 z^9 + 4 z^8 + 12 z^7 + 7 z^6 + 3 z^5 + 3 z^4 + 7 z^3 + 12 z^2 + 4 z + 11$ |
undefined |
