| 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 |
| 7.15.1.0a1.1 |
$15$ |
$x^{15} + 5 x^{6} + 6 x^{5} + 6 x^{4} + 4 x^{3} + x^{2} + 2 x + 4$ |
$7$ |
$15$ |
$1$ |
$0$ |
$C_{15}$ (as 15T1) |
$15$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{15}$ |
$[\ ]^{15}$ |
$[\ ]$ |
$[\ ]$ |
$15$ |
$t^{15} + 5 t^{6} + 6 t^{5} + 6 t^{4} + 4 t^{3} + t^{2} + 2 t + 4$ |
$x - 7$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 7.5.3.10a1.1 |
$15$ |
$( x^{5} + x + 4 )^{3} + 7 x^{2}$ |
$7$ |
$5$ |
$3$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[\ ]_{3}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$15$ |
$t^{5} + t + 4$ |
$x^{3} + 7 t^{2}$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 7.5.3.10a1.2 |
$15$ |
$( x^{5} + x + 4 )^{3} + 7 x$ |
$7$ |
$5$ |
$3$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[\ ]_{3}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$15$ |
$t^{5} + t + 4$ |
$x^{3} + 7 t$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 7.5.3.10a1.3 |
$15$ |
$( x^{5} + x + 4 )^{3} + 7$ |
$7$ |
$5$ |
$3$ |
$10$ |
$C_{15}$ (as 15T1) |
$5$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{5}$ |
$[\ ]_{3}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$15$ |
$t^{5} + t + 4$ |
$x^{3} + 7$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 7.3.5.12a1.1 |
$15$ |
$( x^{3} + 6 x^{2} + 4 )^{5} + 7$ |
$7$ |
$3$ |
$5$ |
$12$ |
$F_5\times C_3$ (as 15T8) |
$12$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}^{12}$ |
$[\ ]_{5}^{12}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$3$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{5} + 7$ |
$[0]$ |
$[4]$ |
$z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ |
undefined |
| 7.1.15.14a1.1 |
$15$ |
$x^{15} + 7$ |
$7$ |
$1$ |
$15$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$[\ ]_{15}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$3$ |
$t + 4$ |
$x^{15} + 7$ |
$[0]$ |
$[4]$ |
$z^{14} + z^{13} + 2 z^7 + 2 z^6 + 1$ |
undefined |
| 7.1.15.14a1.2 |
$15$ |
$x^{15} + 14$ |
$7$ |
$1$ |
$15$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$[\ ]_{15}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$3$ |
$t + 4$ |
$x^{15} + 14$ |
$[0]$ |
$[4]$ |
$z^{14} + z^{13} + 2 z^7 + 2 z^6 + 1$ |
undefined |
| 7.1.15.14a1.3 |
$15$ |
$x^{15} + 21$ |
$7$ |
$1$ |
$15$ |
$14$ |
$F_5\times C_3$ (as 15T8) |
$4$ |
$15$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{15}^{4}$ |
$[\ ]_{15}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$3$ |
$t + 4$ |
$x^{15} + 21$ |
$[0]$ |
$[4]$ |
$z^{14} + z^{13} + 2 z^7 + 2 z^6 + 1$ |
undefined |
