| 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 |
| 41.1.1.0a1.1 |
$1$ |
$x + 35$ |
$41$ |
$1$ |
$1$ |
$0$ |
Trivial (as 1T1) |
$1$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$1$ |
$t + 35$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.2.1.0a1.1 |
$2$ |
$x^{2} + 38 x + 6$ |
$41$ |
$2$ |
$1$ |
$0$ |
$C_2$ (as 2T1) |
$2$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t^{2} + 38 t + 6$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.1.2.1a1.1 |
$2$ |
$x^{2} + 41$ |
$41$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 35$ |
$x^{2} + 41$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.1.2.1a1.2 |
$2$ |
$x^{2} + 246$ |
$41$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 35$ |
$x^{2} + 246$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.3.1.0a1.1 |
$3$ |
$x^{3} + x + 35$ |
$41$ |
$3$ |
$1$ |
$0$ |
$C_3$ (as 3T1) |
$3$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t^{3} + t + 35$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.1.3.2a1.1 |
$3$ |
$x^{3} + 41$ |
$41$ |
$1$ |
$3$ |
$2$ |
$S_3$ (as 3T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 35$ |
$x^{3} + 41$ |
$[0]$ |
$[2]$ |
$z^2 + 3 z + 3$ |
undefined |
| 41.4.1.0a1.1 |
$4$ |
$x^{4} + 23 x + 6$ |
$41$ |
$4$ |
$1$ |
$0$ |
$C_4$ (as 4T1) |
$4$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{4} + 23 t + 6$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.2.2.2a1.1 |
$4$ |
$( x^{2} + 38 x + 6 )^{2} + 41 x$ |
$41$ |
$2$ |
$2$ |
$2$ |
$C_4$ (as 4T1) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 38 t + 6$ |
$x^{2} + 41 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.2.2.2a1.2 |
$4$ |
$( x^{2} + 38 x + 6 )^{2} + 41$ |
$41$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 38 t + 6$ |
$x^{2} + 41$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.1.4.3a1.1 |
$4$ |
$x^{4} + 41$ |
$41$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 35$ |
$x^{4} + 41$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.1.4.3a1.2 |
$4$ |
$x^{4} + 246$ |
$41$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 35$ |
$x^{4} + 246$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.1.4.3a1.3 |
$4$ |
$x^{4} + 451$ |
$41$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 35$ |
$x^{4} + 451$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.1.4.3a1.4 |
$4$ |
$x^{4} + 1476$ |
$41$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 35$ |
$x^{4} + 1476$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.5.1.0a1.1 |
$5$ |
$x^{5} + 40 x^{2} + 14 x + 35$ |
$41$ |
$5$ |
$1$ |
$0$ |
$C_5$ (as 5T1) |
$5$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t^{5} + 40 t^{2} + 14 t + 35$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.1.5.4a1.1 |
$5$ |
$x^{5} + 41$ |
$41$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 35$ |
$x^{5} + 41$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 41.1.5.4a1.2 |
$5$ |
$x^{5} + 246$ |
$41$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 35$ |
$x^{5} + 246$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 41.1.5.4a1.3 |
$5$ |
$x^{5} + 451$ |
$41$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 35$ |
$x^{5} + 451$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 41.1.5.4a1.4 |
$5$ |
$x^{5} + 1025$ |
$41$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 35$ |
$x^{5} + 1025$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 41.1.5.4a1.5 |
$5$ |
$x^{5} + 1476$ |
$41$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 35$ |
$x^{5} + 1476$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 41.6.1.0a1.1 |
$6$ |
$x^{6} + 4 x^{4} + 33 x^{3} + 39 x^{2} + 6 x + 6$ |
$41$ |
$6$ |
$1$ |
$0$ |
$C_6$ (as 6T1) |
$6$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{6} + 4 t^{4} + 33 t^{3} + 39 t^{2} + 6 t + 6$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.3.2.3a1.1 |
$6$ |
$( x^{3} + x + 35 )^{2} + 41 x$ |
$41$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + t + 35$ |
$x^{2} + 41 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.3.2.3a1.2 |
$6$ |
$( x^{3} + x + 35 )^{2} + 41$ |
$41$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + t + 35$ |
$x^{2} + 41$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.2.3.4a1.1 |
$6$ |
$( x^{2} + 38 x + 6 )^{3} + 41 x$ |
$41$ |
$2$ |
$3$ |
$4$ |
$S_3\times C_3$ (as 6T5) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$3$ |
$t^{2} + 38 t + 6$ |
$x^{3} + 123 t + 1435$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 41.2.3.4a1.2 |
$6$ |
$( x^{2} + 38 x + 6 )^{3} + 41$ |
$41$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 38 t + 6$ |
$x^{3} + 41$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 41.1.6.5a1.1 |
$6$ |
$x^{6} + 41$ |
$41$ |
$1$ |
$6$ |
$5$ |
$D_{6}$ (as 6T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[\ ]_{6}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 35$ |
$x^{6} + 41$ |
$[0]$ |
$[2]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 41.1.6.5a1.2 |
$6$ |
$x^{6} + 246$ |
$41$ |
$1$ |
$6$ |
$5$ |
$D_{6}$ (as 6T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[\ ]_{6}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 35$ |
$x^{6} + 246$ |
$[0]$ |
$[2]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 41.7.1.0a1.1 |
$7$ |
$x^{7} + 6 x + 35$ |
$41$ |
$7$ |
$1$ |
$0$ |
$C_7$ (as 7T1) |
$7$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{7}$ |
$[\ ]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t^{7} + 6 t + 35$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.1.7.6a1.1 |
$7$ |
$x^{7} + 41$ |
$41$ |
$1$ |
$7$ |
$6$ |
$D_{7}$ (as 7T2) |
$2$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{2}$ |
$[\ ]_{7}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 35$ |
$x^{7} + 41$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 41.8.1.0a1.1 |
$8$ |
$x^{8} + 5 x^{4} + 32 x^{3} + 20 x^{2} + 6 x + 6$ |
$41$ |
$8$ |
$1$ |
$0$ |
$C_8$ (as 8T1) |
$8$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{8}$ |
$[\ ]^{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{8} + 5 t^{4} + 32 t^{3} + 20 t^{2} + 6 t + 6$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.4.2.4a1.1 |
$8$ |
$( x^{4} + 23 x + 6 )^{2} + 41 x$ |
$41$ |
$4$ |
$2$ |
$4$ |
$C_8$ (as 8T1) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 23 t + 6$ |
$x^{2} + 41 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.4.2.4a1.2 |
$8$ |
$( x^{4} + 23 x + 6 )^{2} + 41$ |
$41$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 23 t + 6$ |
$x^{2} + 41$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.2.4.6a1.1 |
$8$ |
$( x^{2} + 38 x + 6 )^{4} + 41 x$ |
$41$ |
$2$ |
$4$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 38 t + 6$ |
$x^{4} + 41 t$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.2.4.6a1.2 |
$8$ |
$( x^{2} + 38 x + 6 )^{4} + 41$ |
$41$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 38 t + 6$ |
$x^{4} + 41$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.2.4.6a1.3 |
$8$ |
$( x^{2} + 38 x + 6 )^{4} + 123 x + 943$ |
$41$ |
$2$ |
$4$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 38 t + 6$ |
$x^{4} + 123 t + 943$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.2.4.6a1.4 |
$8$ |
$( x^{2} + 38 x + 6 )^{4} + 123 x + 1435$ |
$41$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 38 t + 6$ |
$x^{4} + 123 t + 1435$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 41.1.8.7a1.1 |
$8$ |
$x^{8} + 41$ |
$41$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 35$ |
$x^{8} + 41$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 15 z^4 + 29 z^3 + 15 z^2 + 28 z + 8$ |
undefined |
| 41.1.8.7a1.2 |
$8$ |
$x^{8} + 246$ |
$41$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 35$ |
$x^{8} + 246$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 15 z^4 + 29 z^3 + 15 z^2 + 28 z + 8$ |
undefined |
| 41.1.8.7a1.3 |
$8$ |
$x^{8} + 451$ |
$41$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 35$ |
$x^{8} + 451$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 15 z^4 + 29 z^3 + 15 z^2 + 28 z + 8$ |
undefined |
| 41.1.8.7a1.4 |
$8$ |
$x^{8} + 1025$ |
$41$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 35$ |
$x^{8} + 1025$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 15 z^4 + 29 z^3 + 15 z^2 + 28 z + 8$ |
undefined |
| 41.1.8.7a1.5 |
$8$ |
$x^{8} + 1107$ |
$41$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 35$ |
$x^{8} + 1107$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 15 z^4 + 29 z^3 + 15 z^2 + 28 z + 8$ |
undefined |
| 41.1.8.7a1.6 |
$8$ |
$x^{8} + 1189$ |
$41$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 35$ |
$x^{8} + 1189$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 15 z^4 + 29 z^3 + 15 z^2 + 28 z + 8$ |
undefined |
| 41.1.8.7a1.7 |
$8$ |
$x^{8} + 1476$ |
$41$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 35$ |
$x^{8} + 1476$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 15 z^4 + 29 z^3 + 15 z^2 + 28 z + 8$ |
undefined |
| 41.1.8.7a1.8 |
$8$ |
$x^{8} + 1599$ |
$41$ |
$1$ |
$8$ |
$7$ |
$C_8$ (as 8T1) |
$1$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}$ |
$[\ ]_{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t + 35$ |
$x^{8} + 1599$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 15 z^4 + 29 z^3 + 15 z^2 + 28 z + 8$ |
undefined |
| 41.9.1.0a1.1 |
$9$ |
$x^{9} + 4 x^{3} + 31 x^{2} + 5 x + 35$ |
$41$ |
$9$ |
$1$ |
$0$ |
$C_9$ (as 9T1) |
$9$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{9}$ |
$[\ ]^{9}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{9} + 4 t^{3} + 31 t^{2} + 5 t + 35$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.3.3.6a1.1 |
$9$ |
$( x^{3} + x + 35 )^{3} + 41$ |
$41$ |
$3$ |
$3$ |
$6$ |
$S_3\times C_3$ (as 9T4) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + t + 35$ |
$x^{3} + 41$ |
$[0]$ |
$[2]$ |
$z^2 + 3 z + 3$ |
undefined |
| 41.1.9.8a1.1 |
$9$ |
$x^{9} + 41$ |
$41$ |
$1$ |
$9$ |
$8$ |
$(C_9:C_3):C_2$ (as 9T10) |
$6$ |
$9$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{9}^{6}$ |
$[\ ]_{9}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 35$ |
$x^{9} + 41$ |
$[0]$ |
$[6]$ |
$z^8 + 9 z^7 + 36 z^6 + 2 z^5 + 3 z^4 + 3 z^3 + 2 z^2 + 36 z + 9$ |
undefined |
| 41.10.1.0a1.1 |
$10$ |
$x^{10} + 3 x^{5} + 31 x^{4} + 8 x^{3} + 20 x^{2} + 30 x + 6$ |
$41$ |
$10$ |
$1$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{10}$ |
$[\ ]^{10}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{10} + 3 t^{5} + 31 t^{4} + 8 t^{3} + 20 t^{2} + 30 t + 6$ |
$x - 41$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 41.5.2.5a1.1 |
$10$ |
$( x^{5} + 40 x^{2} + 14 x + 35 )^{2} + 41 x$ |
$41$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + 40 t^{2} + 14 t + 35$ |
$x^{2} + 41 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.5.2.5a1.2 |
$10$ |
$( x^{5} + 40 x^{2} + 14 x + 35 )^{2} + 41$ |
$41$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + 40 t^{2} + 14 t + 35$ |
$x^{2} + 41$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 41.2.5.8a1.1 |
$10$ |
$( x^{2} + 38 x + 6 )^{5} + 41 x$ |
$41$ |
$2$ |
$5$ |
$8$ |
$C_{10}$ (as 10T1) |
$2$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}^{2}$ |
$[\ ]_{5}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{2} + 38 t + 6$ |
$x^{5} + 41 t$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
