| 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 |
| 2.2.10.38a1.53 |
$20$ |
$( x^{2} + x + 1 )^{10} + 4 ( x^{2} + x + 1 )^{5} + 2$ |
$2$ |
$2$ |
$10$ |
$38$ |
$C_2\times F_5$ (as 20T13) |
not computed |
not computed |
$[3]$ |
$[2]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + t + 1$ |
$x^{10} + 4 x^{5} + 2$ |
$[10, 0]$ |
$[2, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 3.2.10.18a1.2 |
$20$ |
$( x^{2} + 2 x + 2 )^{10} + 3$ |
$3$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 2 t + 2$ |
$x^{10} + 3$ |
$[0]$ |
$[2]$ |
$z^9 + z^8 + 1$ |
$[5]$ |
| 5.2.10.30a1.14 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 ( x^{2} + 4 x + 2 )^{6} + 5$ |
$5$ |
$2$ |
$10$ |
$30$ |
$C_2\times F_5$ (as 20T13) |
not computed |
not computed |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 20 x^{6} + 5$ |
$[6, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + 2$ |
undefined |
| 5.2.10.38a1.7 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 50 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$38$ |
$C_2\times F_5$ (as 20T13) |
not computed |
not computed |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 50 x^{2} + 5$ |
$[10, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + 4$ |
undefined |
| 5.2.10.38a1.13 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 100 ( x^{2} + 4 x + 2 )^{2} + 5$ |
$5$ |
$2$ |
$10$ |
$38$ |
$C_2\times F_5$ (as 20T13) |
not computed |
not computed |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + 100 x^{2} + 5$ |
$[10, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^2 + 4$ |
undefined |
| 7.2.10.18a1.2 |
$20$ |
$( x^{2} + 6 x + 3 )^{10} + 7$ |
$7$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 6 t + 3$ |
$x^{10} + 7$ |
$[0]$ |
$[2]$ |
$z^9 + 3 z^8 + 3 z^7 + z^6 + z^2 + 3 z + 3$ |
undefined |
| 13.2.10.18a1.2 |
$20$ |
$( x^{2} + 12 x + 2 )^{10} + 13$ |
$13$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 12 t + 2$ |
$x^{10} + 13$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 6 z^7 + 3 z^6 + 2 z^5 + 5 z^4 + 2 z^3 + 3 z^2 + 6 z + 10$ |
undefined |
| 17.2.10.18a1.2 |
$20$ |
$( x^{2} + 16 x + 3 )^{10} + 17$ |
$17$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 16 t + 3$ |
$x^{10} + 17$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 11 z^7 + z^6 + 6 z^5 + 14 z^4 + 6 z^3 + z^2 + 11 z + 10$ |
undefined |
| 23.2.10.18a1.2 |
$20$ |
$( x^{2} + 21 x + 5 )^{10} + 23$ |
$23$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 21 t + 5$ |
$x^{10} + 23$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 22 z^7 + 5 z^6 + 3 z^5 + 22 z^4 + 3 z^3 + 5 z^2 + 22 z + 10$ |
undefined |
| 37.2.10.18a1.2 |
$20$ |
$( x^{2} + 33 x + 2 )^{10} + 37$ |
$37$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 33 t + 2$ |
$x^{10} + 37$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 8 z^7 + 9 z^6 + 25 z^5 + 30 z^4 + 25 z^3 + 9 z^2 + 8 z + 10$ |
undefined |
| 43.2.10.18a1.2 |
$20$ |
$( x^{2} + 42 x + 3 )^{10} + 43$ |
$43$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 42 t + 3$ |
$x^{10} + 43$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 2 z^7 + 34 z^6 + 38 z^5 + 37 z^4 + 38 z^3 + 34 z^2 + 2 z + 10$ |
undefined |
| 47.2.10.18a1.2 |
$20$ |
$( x^{2} + 45 x + 5 )^{10} + 47$ |
$47$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 45 t + 5$ |
$x^{10} + 47$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 26 z^6 + 22 z^5 + 17 z^4 + 22 z^3 + 26 z^2 + 45 z + 10$ |
undefined |
| 53.2.10.18a1.2 |
$20$ |
$( x^{2} + 49 x + 2 )^{10} + 53$ |
$53$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 49 t + 2$ |
$x^{10} + 53$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 14 z^6 + 51 z^5 + 40 z^4 + 51 z^3 + 14 z^2 + 45 z + 10$ |
undefined |
| 67.2.10.18a1.2 |
$20$ |
$( x^{2} + 63 x + 2 )^{10} + 67$ |
$67$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 63 t + 2$ |
$x^{10} + 67$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 53 z^6 + 9 z^5 + 51 z^4 + 9 z^3 + 53 z^2 + 45 z + 10$ |
undefined |
| 73.2.10.18a1.2 |
$20$ |
$( x^{2} + 70 x + 5 )^{10} + 73$ |
$73$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 70 t + 5$ |
$x^{10} + 73$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 47 z^6 + 64 z^5 + 33 z^4 + 64 z^3 + 47 z^2 + 45 z + 10$ |
undefined |
| 83.2.10.18a1.2 |
$20$ |
$( x^{2} + 82 x + 2 )^{10} + 83$ |
$83$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 82 t + 2$ |
$x^{10} + 83$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 37 z^6 + 44 z^5 + 3 z^4 + 44 z^3 + 37 z^2 + 45 z + 10$ |
undefined |
| 97.2.10.18a1.2 |
$20$ |
$( x^{2} + 96 x + 5 )^{10} + 97$ |
$97$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 96 t + 5$ |
$x^{10} + 97$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 23 z^6 + 16 z^5 + 58 z^4 + 16 z^3 + 23 z^2 + 45 z + 10$ |
undefined |
| 103.2.10.18a1.2 |
$20$ |
$( x^{2} + 102 x + 5 )^{10} + 103$ |
$103$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 102 t + 5$ |
$x^{10} + 103$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 17 z^6 + 4 z^5 + 46 z^4 + 4 z^3 + 17 z^2 + 45 z + 10$ |
undefined |
| 107.2.10.18a1.2 |
$20$ |
$( x^{2} + 103 x + 2 )^{10} + 107$ |
$107$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 103 t + 2$ |
$x^{10} + 107$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 13 z^6 + 103 z^5 + 38 z^4 + 103 z^3 + 13 z^2 + 45 z + 10$ |
undefined |
| 113.2.10.18a1.2 |
$20$ |
$( x^{2} + 101 x + 3 )^{10} + 113$ |
$113$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 101 t + 3$ |
$x^{10} + 113$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 7 z^6 + 97 z^5 + 26 z^4 + 97 z^3 + 7 z^2 + 45 z + 10$ |
undefined |
| 127.2.10.18a1.2 |
$20$ |
$( x^{2} + 126 x + 3 )^{10} + 127$ |
$127$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 126 t + 3$ |
$x^{10} + 127$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 83 z^5 + 125 z^4 + 83 z^3 + 120 z^2 + 45 z + 10$ |
undefined |
| 137.2.10.18a1.2 |
$20$ |
$( x^{2} + 131 x + 3 )^{10} + 137$ |
$137$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 131 t + 3$ |
$x^{10} + 137$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 73 z^5 + 115 z^4 + 73 z^3 + 120 z^2 + 45 z + 10$ |
undefined |
| 157.2.10.18a1.2 |
$20$ |
$( x^{2} + 152 x + 5 )^{10} + 157$ |
$157$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 152 t + 5$ |
$x^{10} + 157$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 53 z^5 + 95 z^4 + 53 z^3 + 120 z^2 + 45 z + 10$ |
undefined |
| 163.2.10.18a1.2 |
$20$ |
$( x^{2} + 159 x + 2 )^{10} + 163$ |
$163$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 159 t + 2$ |
$x^{10} + 163$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 47 z^5 + 89 z^4 + 47 z^3 + 120 z^2 + 45 z + 10$ |
undefined |
| 167.2.10.18a1.2 |
$20$ |
$( x^{2} + 166 x + 5 )^{10} + 167$ |
$167$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 166 t + 5$ |
$x^{10} + 167$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 43 z^5 + 85 z^4 + 43 z^3 + 120 z^2 + 45 z + 10$ |
undefined |
| 173.2.10.18a1.2 |
$20$ |
$( x^{2} + 169 x + 2 )^{10} + 173$ |
$173$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 169 t + 2$ |
$x^{10} + 173$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 37 z^5 + 79 z^4 + 37 z^3 + 120 z^2 + 45 z + 10$ |
undefined |
| 193.2.10.18a1.2 |
$20$ |
$( x^{2} + 192 x + 5 )^{10} + 193$ |
$193$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 192 t + 5$ |
$x^{10} + 193$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 17 z^5 + 59 z^4 + 17 z^3 + 120 z^2 + 45 z + 10$ |
undefined |
| 197.2.10.18a1.2 |
$20$ |
$( x^{2} + 192 x + 2 )^{10} + 197$ |
$197$ |
$2$ |
$10$ |
$18$ |
$C_2\times F_5$ (as 20T13) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 192 t + 2$ |
$x^{10} + 197$ |
$[0]$ |
$[2]$ |
$z^9 + 10 z^8 + 45 z^7 + 120 z^6 + 13 z^5 + 55 z^4 + 13 z^3 + 120 z^2 + 45 z + 10$ |
undefined |
