| 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 |
| 61.1.1.0a1.1 |
$1$ |
$x + 59$ |
$61$ |
$1$ |
$1$ |
$0$ |
Trivial (as 1T1) |
$1$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$1$ |
$t + 59$ |
$x - 61$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 61.2.1.0a1.1 |
$2$ |
$x^{2} + 60 x + 2$ |
$61$ |
$2$ |
$1$ |
$0$ |
$C_2$ (as 2T1) |
$2$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t^{2} + 60 t + 2$ |
$x - 61$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 61.1.2.1a1.1 |
$2$ |
$x^{2} + 61$ |
$61$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 59$ |
$x^{2} + 61$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.1.2.1a1.2 |
$2$ |
$x^{2} + 122$ |
$61$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 59$ |
$x^{2} + 122$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.3.1.0a1.1 |
$3$ |
$x^{3} + 7 x + 59$ |
$61$ |
$3$ |
$1$ |
$0$ |
$C_3$ (as 3T1) |
$3$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t^{3} + 7 t + 59$ |
$x - 61$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 61.1.3.2a1.1 |
$3$ |
$x^{3} + 61$ |
$61$ |
$1$ |
$3$ |
$2$ |
$C_3$ (as 3T1) |
$1$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t + 59$ |
$x^{3} + 61$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 61.1.3.2a1.2 |
$3$ |
$x^{3} + 122$ |
$61$ |
$1$ |
$3$ |
$2$ |
$C_3$ (as 3T1) |
$1$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t + 59$ |
$x^{3} + 122$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 61.1.3.2a1.3 |
$3$ |
$x^{3} + 244$ |
$61$ |
$1$ |
$3$ |
$2$ |
$C_3$ (as 3T1) |
$1$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}$ |
$[\ ]_{3}$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t + 59$ |
$x^{3} + 244$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 61.4.1.0a1.1 |
$4$ |
$x^{4} + 3 x^{2} + 40 x + 2$ |
$61$ |
$4$ |
$1$ |
$0$ |
$C_4$ (as 4T1) |
$4$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{4} + 3 t^{2} + 40 t + 2$ |
$x - 61$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 61.2.2.2a1.1 |
$4$ |
$( x^{2} + 60 x + 2 )^{2} + 61 x$ |
$61$ |
$2$ |
$2$ |
$2$ |
$C_4$ (as 4T1) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 60 t + 2$ |
$x^{2} + 61 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.2.2.2a1.2 |
$4$ |
$( x^{2} + 60 x + 2 )^{2} + 61$ |
$61$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 60 t + 2$ |
$x^{2} + 61$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.1.4.3a1.1 |
$4$ |
$x^{4} + 61$ |
$61$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 59$ |
$x^{4} + 61$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 61.1.4.3a1.2 |
$4$ |
$x^{4} + 122$ |
$61$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 59$ |
$x^{4} + 122$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 61.1.4.3a1.3 |
$4$ |
$x^{4} + 244$ |
$61$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 59$ |
$x^{4} + 244$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 61.1.4.3a1.4 |
$4$ |
$x^{4} + 488$ |
$61$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 59$ |
$x^{4} + 488$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 61.5.1.0a1.1 |
$5$ |
$x^{5} + 12 x + 59$ |
$61$ |
$5$ |
$1$ |
$0$ |
$C_5$ (as 5T1) |
$5$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t^{5} + 12 t + 59$ |
$x - 61$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 61.1.5.4a1.1 |
$5$ |
$x^{5} + 61$ |
$61$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 59$ |
$x^{5} + 61$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 61.1.5.4a1.2 |
$5$ |
$x^{5} + 122$ |
$61$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 59$ |
$x^{5} + 122$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 61.1.5.4a1.3 |
$5$ |
$x^{5} + 244$ |
$61$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 59$ |
$x^{5} + 244$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 61.1.5.4a1.4 |
$5$ |
$x^{5} + 488$ |
$61$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 59$ |
$x^{5} + 488$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 61.1.5.4a1.5 |
$5$ |
$x^{5} + 976$ |
$61$ |
$1$ |
$5$ |
$4$ |
$C_5$ (as 5T1) |
$1$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}$ |
$[\ ]_{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t + 59$ |
$x^{5} + 976$ |
$[0]$ |
$[1]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 61.6.1.0a1.1 |
$6$ |
$x^{6} + 49 x^{3} + 3 x^{2} + 29 x + 2$ |
$61$ |
$6$ |
$1$ |
$0$ |
$C_6$ (as 6T1) |
$6$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{6} + 49 t^{3} + 3 t^{2} + 29 t + 2$ |
$x - 61$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 61.3.2.3a1.1 |
$6$ |
$( x^{3} + 7 x + 59 )^{2} + 61 x$ |
$61$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + 7 t + 59$ |
$x^{2} + 61 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.3.2.3a1.2 |
$6$ |
$( x^{3} + 7 x + 59 )^{2} + 61$ |
$61$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + 7 t + 59$ |
$x^{2} + 61$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.2.3.4a1.1 |
$6$ |
$( x^{2} + 60 x + 2 )^{3} + 61 x$ |
$61$ |
$2$ |
$3$ |
$4$ |
$C_6$ (as 6T1) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 60 t + 2$ |
$x^{3} + 61 t$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 61.2.3.4a1.2 |
$6$ |
$( x^{2} + 60 x + 2 )^{3} + 61$ |
$61$ |
$2$ |
$3$ |
$4$ |
$C_6$ (as 6T1) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 60 t + 2$ |
$x^{3} + 61$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 61.2.3.4a1.3 |
$6$ |
$( x^{2} + 60 x + 2 )^{3} + 61 x + 3599$ |
$61$ |
$2$ |
$3$ |
$4$ |
$C_6$ (as 6T1) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 60 t + 2$ |
$x^{3} + 61 t + 3599$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 61.1.6.5a1.1 |
$6$ |
$x^{6} + 61$ |
$61$ |
$1$ |
$6$ |
$5$ |
$C_6$ (as 6T1) |
$1$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 59$ |
$x^{6} + 61$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 61.1.6.5a1.2 |
$6$ |
$x^{6} + 122$ |
$61$ |
$1$ |
$6$ |
$5$ |
$C_6$ (as 6T1) |
$1$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 59$ |
$x^{6} + 122$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 61.1.6.5a1.3 |
$6$ |
$x^{6} + 244$ |
$61$ |
$1$ |
$6$ |
$5$ |
$C_6$ (as 6T1) |
$1$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 59$ |
$x^{6} + 244$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 61.1.6.5a1.4 |
$6$ |
$x^{6} + 488$ |
$61$ |
$1$ |
$6$ |
$5$ |
$C_6$ (as 6T1) |
$1$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 59$ |
$x^{6} + 488$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 61.1.6.5a1.5 |
$6$ |
$x^{6} + 976$ |
$61$ |
$1$ |
$6$ |
$5$ |
$C_6$ (as 6T1) |
$1$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 59$ |
$x^{6} + 976$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 61.1.6.5a1.6 |
$6$ |
$x^{6} + 1952$ |
$61$ |
$1$ |
$6$ |
$5$ |
$C_6$ (as 6T1) |
$1$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 59$ |
$x^{6} + 1952$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 61.7.1.0a1.1 |
$7$ |
$x^{7} + 2 x + 59$ |
$61$ |
$7$ |
$1$ |
$0$ |
$C_7$ (as 7T1) |
$7$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{7}$ |
$[\ ]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t^{7} + 2 t + 59$ |
$x - 61$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 61.1.7.6a1.1 |
$7$ |
$x^{7} + 61$ |
$61$ |
$1$ |
$7$ |
$6$ |
$F_7$ (as 7T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 59$ |
$x^{7} + 61$ |
$[0]$ |
$[6]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 61.8.1.0a1.1 |
$8$ |
$x^{8} + 57 x^{3} + x^{2} + 56 x + 2$ |
$61$ |
$8$ |
$1$ |
$0$ |
$C_8$ (as 8T1) |
$8$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{8}$ |
$[\ ]^{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{8} + 57 t^{3} + t^{2} + 56 t + 2$ |
$x - 61$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 61.4.2.4a1.1 |
$8$ |
$( x^{4} + 3 x^{2} + 40 x + 2 )^{2} + 61 x$ |
$61$ |
$4$ |
$2$ |
$4$ |
$C_8$ (as 8T1) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 3 t^{2} + 40 t + 2$ |
$x^{2} + 61 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.4.2.4a1.2 |
$8$ |
$( x^{4} + 3 x^{2} + 40 x + 2 )^{2} + 61$ |
$61$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 3 t^{2} + 40 t + 2$ |
$x^{2} + 61$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 61.2.4.6a1.1 |
$8$ |
$( x^{2} + 60 x + 2 )^{4} + 61 x$ |
$61$ |
$2$ |
$4$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 60 t + 2$ |
$x^{4} + 61 t$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 61.2.4.6a1.2 |
$8$ |
$( x^{2} + 60 x + 2 )^{4} + 61$ |
$61$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 60 t + 2$ |
$x^{4} + 61$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 61.2.4.6a1.3 |
$8$ |
$( x^{2} + 60 x + 2 )^{4} + 61 x + 3599$ |
$61$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 60 t + 2$ |
$x^{4} + 61 t + 3599$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 61.2.4.6a1.4 |
$8$ |
$( x^{2} + 60 x + 2 )^{4} + 3660 x + 3599$ |
$61$ |
$2$ |
$4$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 60 t + 2$ |
$x^{4} + 3660 t + 3599$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 61.1.8.7a1.1 |
$8$ |
$x^{8} + 61$ |
$61$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 59$ |
$x^{8} + 61$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 9 z^3 + 56 z^2 + 28 z + 8$ |
undefined |
| 61.1.8.7a1.2 |
$8$ |
$x^{8} + 122$ |
$61$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 59$ |
$x^{8} + 122$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 9 z^3 + 56 z^2 + 28 z + 8$ |
undefined |
| 61.1.8.7a1.3 |
$8$ |
$x^{8} + 244$ |
$61$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 59$ |
$x^{8} + 244$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 9 z^3 + 56 z^2 + 28 z + 8$ |
undefined |
| 61.1.8.7a1.4 |
$8$ |
$x^{8} + 488$ |
$61$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 59$ |
$x^{8} + 488$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 9 z^3 + 56 z^2 + 28 z + 8$ |
undefined |
| 61.9.1.0a1.1 |
$9$ |
$x^{9} + 9 x^{3} + 50 x^{2} + 18 x + 59$ |
$61$ |
$9$ |
$1$ |
$0$ |
$C_9$ (as 9T1) |
$9$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{9}$ |
$[\ ]^{9}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{9} + 9 t^{3} + 50 t^{2} + 18 t + 59$ |
$x - 61$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 61.3.3.6a1.1 |
$9$ |
$( x^{3} + 7 x + 59 )^{3} + 61 x^{2}$ |
$61$ |
$3$ |
$3$ |
$6$ |
$C_9$ (as 9T1) |
$3$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{3}$ |
$[\ ]_{3}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{3} + 7 t + 59$ |
$x^{3} + 61 t^{2}$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 61.3.3.6a1.2 |
$9$ |
$( x^{3} + 7 x + 59 )^{3} + 61 x$ |
$61$ |
$3$ |
$3$ |
$6$ |
$C_9$ (as 9T1) |
$3$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{3}$ |
$[\ ]_{3}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{3} + 7 t + 59$ |
$x^{3} + 61 t$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 61.3.3.6a1.3 |
$9$ |
$( x^{3} + 7 x + 59 )^{3} + 61$ |
$61$ |
$3$ |
$3$ |
$6$ |
$C_3^2$ (as 9T2) |
$3$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{3}$ |
$[\ ]_{3}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{3} + 7 t + 59$ |
$x^{3} + 61$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
