| 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 |
| 53.1.1.0a1.1 |
$1$ |
$x + 51$ |
$53$ |
$1$ |
$1$ |
$0$ |
Trivial (as 1T1) |
$1$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$1$ |
$t + 51$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.2.1.0a1.1 |
$2$ |
$x^{2} + 49 x + 2$ |
$53$ |
$2$ |
$1$ |
$0$ |
$C_2$ (as 2T1) |
$2$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t^{2} + 49 t + 2$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.1.2.1a1.1 |
$2$ |
$x^{2} + 53$ |
$53$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 51$ |
$x^{2} + 53$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.1.2.1a1.2 |
$2$ |
$x^{2} + 106$ |
$53$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 51$ |
$x^{2} + 106$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.3.1.0a1.1 |
$3$ |
$x^{3} + 3 x + 51$ |
$53$ |
$3$ |
$1$ |
$0$ |
$C_3$ (as 3T1) |
$3$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t^{3} + 3 t + 51$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.1.3.2a1.1 |
$3$ |
$x^{3} + 53$ |
$53$ |
$1$ |
$3$ |
$2$ |
$S_3$ (as 3T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 51$ |
$x^{3} + 53$ |
$[0]$ |
$[2]$ |
$z^2 + 3 z + 3$ |
undefined |
| 53.4.1.0a1.1 |
$4$ |
$x^{4} + 9 x^{2} + 38 x + 2$ |
$53$ |
$4$ |
$1$ |
$0$ |
$C_4$ (as 4T1) |
$4$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{4} + 9 t^{2} + 38 t + 2$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.2.2.2a1.1 |
$4$ |
$( x^{2} + 49 x + 2 )^{2} + 53 x$ |
$53$ |
$2$ |
$2$ |
$2$ |
$C_4$ (as 4T1) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 49 t + 2$ |
$x^{2} + 53 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.2.2.2a1.2 |
$4$ |
$( x^{2} + 49 x + 2 )^{2} + 53$ |
$53$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 49 t + 2$ |
$x^{2} + 53$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.1.4.3a1.1 |
$4$ |
$x^{4} + 53$ |
$53$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 51$ |
$x^{4} + 53$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 53.1.4.3a1.2 |
$4$ |
$x^{4} + 106$ |
$53$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 51$ |
$x^{4} + 106$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 53.1.4.3a1.3 |
$4$ |
$x^{4} + 212$ |
$53$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 51$ |
$x^{4} + 212$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 53.1.4.3a1.4 |
$4$ |
$x^{4} + 424$ |
$53$ |
$1$ |
$4$ |
$3$ |
$C_4$ (as 4T1) |
$1$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}$ |
$[\ ]_{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t + 51$ |
$x^{4} + 424$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 53.5.1.0a1.1 |
$5$ |
$x^{5} + 3 x + 51$ |
$53$ |
$5$ |
$1$ |
$0$ |
$C_5$ (as 5T1) |
$5$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t^{5} + 3 t + 51$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.1.5.4a1.1 |
$5$ |
$x^{5} + 53$ |
$53$ |
$1$ |
$5$ |
$4$ |
$F_5$ (as 5T3) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$[\ ]_{5}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$1$ |
$t + 51$ |
$x^{5} + 53$ |
$[0]$ |
$[4]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 53.6.1.0a1.1 |
$6$ |
$x^{6} + x^{4} + 7 x^{3} + 4 x^{2} + 45 x + 2$ |
$53$ |
$6$ |
$1$ |
$0$ |
$C_6$ (as 6T1) |
$6$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{6} + t^{4} + 7 t^{3} + 4 t^{2} + 45 t + 2$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.3.2.3a1.1 |
$6$ |
$( x^{3} + 3 x + 51 )^{2} + 53 x$ |
$53$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + 3 t + 51$ |
$x^{2} + 53 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.3.2.3a1.2 |
$6$ |
$( x^{3} + 3 x + 51 )^{2} + 53$ |
$53$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + 3 t + 51$ |
$x^{2} + 53$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.2.3.4a1.1 |
$6$ |
$( x^{2} + 49 x + 2 )^{3} + 53 x$ |
$53$ |
$2$ |
$3$ |
$4$ |
$S_3\times C_3$ (as 6T5) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$3$ |
$t^{2} + 49 t + 2$ |
$x^{3} + 53 t$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 53.2.3.4a1.2 |
$6$ |
$( x^{2} + 49 x + 2 )^{3} + 53$ |
$53$ |
$2$ |
$3$ |
$4$ |
$S_3$ (as 6T2) |
$2$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{2}$ |
$[\ ]_{3}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 49 t + 2$ |
$x^{3} + 53$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 53.1.6.5a1.1 |
$6$ |
$x^{6} + 53$ |
$53$ |
$1$ |
$6$ |
$5$ |
$D_{6}$ (as 6T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[\ ]_{6}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 51$ |
$x^{6} + 53$ |
$[0]$ |
$[2]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 53.1.6.5a1.2 |
$6$ |
$x^{6} + 106$ |
$53$ |
$1$ |
$6$ |
$5$ |
$D_{6}$ (as 6T3) |
$2$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{2}$ |
$[\ ]_{6}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 51$ |
$x^{6} + 106$ |
$[0]$ |
$[2]$ |
$z^5 + 6 z^4 + 15 z^3 + 20 z^2 + 15 z + 6$ |
undefined |
| 53.7.1.0a1.1 |
$7$ |
$x^{7} + 9 x + 51$ |
$53$ |
$7$ |
$1$ |
$0$ |
$C_7$ (as 7T1) |
$7$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{7}$ |
$[\ ]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$7$ |
$t^{7} + 9 t + 51$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.1.7.6a1.1 |
$7$ |
$x^{7} + 53$ |
$53$ |
$1$ |
$7$ |
$6$ |
$C_7:C_3$ (as 7T3) |
$3$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{3}$ |
$[\ ]_{7}^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$1$ |
$t + 51$ |
$x^{7} + 53$ |
$[0]$ |
$[3]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 53.8.1.0a1.1 |
$8$ |
$x^{8} + 8 x^{4} + 29 x^{3} + 18 x^{2} + x + 2$ |
$53$ |
$8$ |
$1$ |
$0$ |
$C_8$ (as 8T1) |
$8$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{8}$ |
$[\ ]^{8}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{8} + 8 t^{4} + 29 t^{3} + 18 t^{2} + t + 2$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.4.2.4a1.1 |
$8$ |
$( x^{4} + 9 x^{2} + 38 x + 2 )^{2} + 53 x$ |
$53$ |
$4$ |
$2$ |
$4$ |
$C_8$ (as 8T1) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 9 t^{2} + 38 t + 2$ |
$x^{2} + 53 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.4.2.4a1.2 |
$8$ |
$( x^{4} + 9 x^{2} + 38 x + 2 )^{2} + 53$ |
$53$ |
$4$ |
$2$ |
$4$ |
$C_4\times C_2$ (as 8T2) |
$4$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{4}$ |
$[\ ]_{2}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{4} + 9 t^{2} + 38 t + 2$ |
$x^{2} + 53$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.2.4.6a1.1 |
$8$ |
$( x^{2} + 49 x + 2 )^{4} + 53 x$ |
$53$ |
$2$ |
$4$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 49 t + 2$ |
$x^{4} + 53 t$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 53.2.4.6a1.2 |
$8$ |
$( x^{2} + 49 x + 2 )^{4} + 53$ |
$53$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 49 t + 2$ |
$x^{4} + 53$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 53.2.4.6a1.3 |
$8$ |
$( x^{2} + 49 x + 2 )^{4} + 742 x + 2385$ |
$53$ |
$2$ |
$4$ |
$6$ |
$C_8$ (as 8T1) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 49 t + 2$ |
$x^{4} + 742 t + 2385$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 53.2.4.6a1.4 |
$8$ |
$( x^{2} + 49 x + 2 )^{4} + 212 x + 2703$ |
$53$ |
$2$ |
$4$ |
$6$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + 49 t + 2$ |
$x^{4} + 212 t + 2703$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 53.1.8.7a1.1 |
$8$ |
$x^{8} + 53$ |
$53$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 51$ |
$x^{8} + 53$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 28 z^5 + 3 z^4 + 17 z^3 + 3 z^2 + 28 z + 8$ |
undefined |
| 53.1.8.7a1.2 |
$8$ |
$x^{8} + 106$ |
$53$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 51$ |
$x^{8} + 106$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 28 z^5 + 3 z^4 + 17 z^3 + 3 z^2 + 28 z + 8$ |
undefined |
| 53.1.8.7a1.3 |
$8$ |
$x^{8} + 212$ |
$53$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 51$ |
$x^{8} + 212$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 28 z^5 + 3 z^4 + 17 z^3 + 3 z^2 + 28 z + 8$ |
undefined |
| 53.1.8.7a1.4 |
$8$ |
$x^{8} + 424$ |
$53$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 51$ |
$x^{8} + 424$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 28 z^5 + 3 z^4 + 17 z^3 + 3 z^2 + 28 z + 8$ |
undefined |
| 53.9.1.0a1.1 |
$9$ |
$x^{9} + 13 x^{2} + 5 x + 51$ |
$53$ |
$9$ |
$1$ |
$0$ |
$C_9$ (as 9T1) |
$9$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{9}$ |
$[\ ]^{9}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{9} + 13 t^{2} + 5 t + 51$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.3.3.6a1.1 |
$9$ |
$( x^{3} + 3 x + 51 )^{3} + 53$ |
$53$ |
$3$ |
$3$ |
$6$ |
$S_3\times C_3$ (as 9T4) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 3 t + 51$ |
$x^{3} + 53$ |
$[0]$ |
$[2]$ |
$z^2 + 3 z + 3$ |
undefined |
| 53.1.9.8a1.1 |
$9$ |
$x^{9} + 53$ |
$53$ |
$1$ |
$9$ |
$8$ |
$D_{9}$ (as 9T3) |
$2$ |
$9$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{9}^{2}$ |
$[\ ]_{9}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 51$ |
$x^{9} + 53$ |
$[0]$ |
$[2]$ |
$z^8 + 9 z^7 + 36 z^6 + 31 z^5 + 20 z^4 + 20 z^3 + 31 z^2 + 36 z + 9$ |
undefined |
| 53.10.1.0a1.1 |
$10$ |
$x^{10} + x^{6} + x^{4} + 27 x^{3} + 15 x^{2} + 29 x + 2$ |
$53$ |
$10$ |
$1$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{10}$ |
$[\ ]^{10}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{10} + t^{6} + t^{4} + 27 t^{3} + 15 t^{2} + 29 t + 2$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.5.2.5a1.1 |
$10$ |
$( x^{5} + 3 x + 51 )^{2} + 53 x$ |
$53$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + 3 t + 51$ |
$x^{2} + 53 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.5.2.5a1.2 |
$10$ |
$( x^{5} + 3 x + 51 )^{2} + 53$ |
$53$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + 3 t + 51$ |
$x^{2} + 53$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.2.5.8a1.1 |
$10$ |
$( x^{2} + 49 x + 2 )^{5} + 53$ |
$53$ |
$2$ |
$5$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$[\ ]_{5}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t^{2} + 49 t + 2$ |
$x^{5} + 53$ |
$[0]$ |
$[2]$ |
$z^4 + 5 z^3 + 10 z^2 + 10 z + 5$ |
undefined |
| 53.1.10.9a1.1 |
$10$ |
$x^{10} + 53$ |
$53$ |
$1$ |
$10$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$2$ |
$t + 51$ |
$x^{10} + 53$ |
$[0]$ |
$[4]$ |
$z^9 + 10 z^8 + 45 z^7 + 14 z^6 + 51 z^5 + 40 z^4 + 51 z^3 + 14 z^2 + 45 z + 10$ |
undefined |
| 53.1.10.9a1.2 |
$10$ |
$x^{10} + 106$ |
$53$ |
$1$ |
$10$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$2$ |
$t + 51$ |
$x^{10} + 106$ |
$[0]$ |
$[4]$ |
$z^9 + 10 z^8 + 45 z^7 + 14 z^6 + 51 z^5 + 40 z^4 + 51 z^3 + 14 z^2 + 45 z + 10$ |
undefined |
| 53.11.1.0a1.1 |
$11$ |
$x^{11} + 15 x + 51$ |
$53$ |
$11$ |
$1$ |
$0$ |
$C_{11}$ (as 11T1) |
$11$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{11}$ |
$[\ ]^{11}$ |
$[\ ]$ |
$[\ ]$ |
$11$ |
$t^{11} + 15 t + 51$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.1.11.10a1.1 |
$11$ |
$x^{11} + 53$ |
$53$ |
$1$ |
$11$ |
$10$ |
$C_{11}:C_5$ (as 11T3) |
$5$ |
$11$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{11}^{5}$ |
$[\ ]_{11}^{5}$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$1$ |
$t + 51$ |
$x^{11} + 53$ |
$[0]$ |
$[5]$ |
$z^{10} + 11 z^9 + 2 z^8 + 6 z^7 + 12 z^6 + 38 z^5 + 38 z^4 + 12 z^3 + 6 z^2 + 2 z + 11$ |
undefined |
| 53.12.1.0a1.1 |
$12$ |
$x^{12} + 2 x^{8} + 34 x^{7} + 4 x^{6} + 13 x^{5} + 10 x^{4} + 42 x^{3} + 34 x^{2} + 41 x + 2$ |
$53$ |
$12$ |
$1$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{12}$ |
$[\ ]^{12}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{12} + 2 t^{8} + 34 t^{7} + 4 t^{6} + 13 t^{5} + 10 t^{4} + 42 t^{3} + 34 t^{2} + 41 t + 2$ |
$x - 53$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 53.6.2.6a1.1 |
$12$ |
$( x^{6} + x^{4} + 7 x^{3} + 4 x^{2} + 45 x + 2 )^{2} + 53 x$ |
$53$ |
$6$ |
$2$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[\ ]_{2}^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + t^{4} + 7 t^{3} + 4 t^{2} + 45 t + 2$ |
$x^{2} + 53 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.6.2.6a1.2 |
$12$ |
$( x^{6} + x^{4} + 7 x^{3} + 4 x^{2} + 45 x + 2 )^{2} + 53$ |
$53$ |
$6$ |
$2$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[\ ]_{2}^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + t^{4} + 7 t^{3} + 4 t^{2} + 45 t + 2$ |
$x^{2} + 53$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 53.4.3.8a1.1 |
$12$ |
$( x^{4} + 9 x^{2} + 38 x + 2 )^{3} + 53 x$ |
$53$ |
$4$ |
$3$ |
$8$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{12}$ |
$[\ ]_{3}^{12}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t^{4} + 9 t^{2} + 38 t + 2$ |
$x^{3} + 53 t$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
