| 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 |
| 127.16.1.0a1.1 |
$16$ |
$x^{16} - x + 3$ |
$127$ |
$16$ |
$1$ |
$0$ |
$C_{16}$ (as 16T1) |
$16$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{16}$ |
$[\ ]^{16}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{16} - t + 3$ |
$x - 127$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 127.8.2.8a1.1 |
$16$ |
$( x^{8} + 3 x^{4} + 104 x^{3} + 55 x^{2} + 8 x + 3 )^{2} + 127 x$ |
$127$ |
$8$ |
$2$ |
$8$ |
$C_{16}$ (as 16T1) |
$8$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{8}$ |
$[\ ]_{2}^{8}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{8} + 3 t^{4} + 104 t^{3} + 55 t^{2} + 8 t + 3$ |
$x^{2} + 127 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 127.8.2.8a1.2 |
$16$ |
$( x^{8} + 3 x^{4} + 104 x^{3} + 55 x^{2} + 8 x + 3 )^{2} + 127$ |
$127$ |
$8$ |
$2$ |
$8$ |
$C_8\times C_2$ (as 16T5) |
$8$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{8}$ |
$[\ ]_{2}^{8}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{8} + 3 t^{4} + 104 t^{3} + 55 t^{2} + 8 t + 3$ |
$x^{2} + 127$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 127.4.4.12a1.1 |
$16$ |
$( x^{4} + 2 x^{2} + 97 x + 3 )^{4} + 127 x^{2}$ |
$127$ |
$4$ |
$4$ |
$12$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + 2 t^{2} + 97 t + 3$ |
$x^{4} + 127 t^{2}$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 127.4.4.12a1.2 |
$16$ |
$( x^{4} + 2 x^{2} + 97 x + 3 )^{4} + 127 x$ |
$127$ |
$4$ |
$4$ |
$12$ |
$C_{16} : C_2$ (as 16T22) |
$8$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{8}$ |
$[\ ]_{4}^{8}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$8$ |
$t^{4} + 2 t^{2} + 97 t + 3$ |
$x^{4} + 127 t^{3}$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 127.4.4.12a1.3 |
$16$ |
$( x^{4} + 2 x^{2} + 97 x + 3 )^{4} + 127$ |
$127$ |
$4$ |
$4$ |
$12$ |
$C_4:C_4$ (as 16T8) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + 2 t^{2} + 97 t + 3$ |
$x^{4} + 127$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 127.2.8.14a1.1 |
$16$ |
$( x^{2} + 126 x + 3 )^{8} + 127 x$ |
$127$ |
$2$ |
$8$ |
$14$ |
$C_8.C_8$ (as 16T124) |
$8$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{8}$ |
$[\ ]_{8}^{8}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$8$ |
$t^{2} + 126 t + 3$ |
$x^{8} + 1651 t + 10033$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ |
undefined |
| 127.2.8.14a1.2 |
$16$ |
$( x^{2} + 126 x + 3 )^{8} + 127$ |
$127$ |
$2$ |
$8$ |
$14$ |
$D_{8}$ (as 16T13) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 126 t + 3$ |
$x^{8} + 127$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ |
undefined |
| 127.2.8.14a1.3 |
$16$ |
$( x^{2} + 126 x + 3 )^{8} + 15494 x + 762$ |
$127$ |
$2$ |
$8$ |
$14$ |
$Q_{16}$ (as 16T14) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 126 t + 3$ |
$x^{8} + 15494 t + 762$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ |
undefined |
| 127.2.8.14a1.4 |
$16$ |
$( x^{2} + 126 x + 3 )^{8} + 127 x + 1905$ |
$127$ |
$2$ |
$8$ |
$14$ |
$C_8.C_8$ (as 16T124) |
$8$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{8}$ |
$[\ ]_{8}^{8}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$8$ |
$t^{2} + 126 t + 3$ |
$x^{8} + 15875 t + 15748$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ |
undefined |
| 127.2.8.14a1.5 |
$16$ |
$( x^{2} + 126 x + 3 )^{8} + 127 x + 15748$ |
$127$ |
$2$ |
$8$ |
$14$ |
$C_8.C_4$ (as 16T49) |
$4$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{4}$ |
$[\ ]_{8}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$8$ |
$t^{2} + 126 t + 3$ |
$x^{8} + 2032 t + 15748$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 56 z^4 + 70 z^3 + 56 z^2 + 28 z + 8$ |
undefined |
| 127.1.16.15a1.1 |
$16$ |
$x^{16} + 127$ |
$127$ |
$1$ |
$16$ |
$15$ |
$D_{16}$ (as 16T56) |
$2$ |
$16$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{16}^{2}$ |
$[\ ]_{16}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 124$ |
$x^{16} + 127$ |
$[0]$ |
$[2]$ |
$z^{15} + 16 z^{14} + 120 z^{13} + 52 z^{12} + 42 z^{11} + 50 z^{10} + 7 z^9 + 10 z^8 + 43 z^7 + 10 z^6 + 7 z^5 + 50 z^4 + 42 z^3 + 52 z^2 + 120 z + 16$ |
undefined |
| 127.1.16.15a1.2 |
$16$ |
$x^{16} + 381$ |
$127$ |
$1$ |
$16$ |
$15$ |
$D_{16}$ (as 16T56) |
$2$ |
$16$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{16}^{2}$ |
$[\ ]_{16}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 124$ |
$x^{16} + 381$ |
$[0]$ |
$[2]$ |
$z^{15} + 16 z^{14} + 120 z^{13} + 52 z^{12} + 42 z^{11} + 50 z^{10} + 7 z^9 + 10 z^8 + 43 z^7 + 10 z^6 + 7 z^5 + 50 z^4 + 42 z^3 + 52 z^2 + 120 z + 16$ |
undefined |
