| 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 |
| 2.1.10.10a1.2 |
$10$ |
$x^{10} + 2 x^{2} + 2 x + 2$ |
$2$ |
$1$ |
$10$ |
$10$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{6}{5}]$ |
$[\frac{1}{5}]$ |
$[\frac{6}{5}, \frac{6}{5}, \frac{6}{5}, \frac{6}{5}]_{5}^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5}]_{5}^{4}$ |
$[\frac{6}{5},\frac{6}{5},\frac{6}{5}]^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 11]$ |
| 2.1.10.12a1.1 |
$10$ |
$x^{10} + 2 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{8}{5}]$ |
$[\frac{3}{5}]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 13]$ |
| 2.1.10.12a1.3 |
$10$ |
$x^{10} + 2 x^{5} + 2 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{8}{5}]$ |
$[\frac{3}{5}]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 13]$ |
| 2.1.10.16a1.1 |
$10$ |
$x^{10} + 2 x^{7} + 2$ |
$2$ |
$1$ |
$10$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{12}{5}]$ |
$[\frac{7}{5}]$ |
$[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ |
$[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 2$ |
$[7, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.16a1.3 |
$10$ |
$x^{10} + 2 x^{7} + 4 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{12}{5}]$ |
$[\frac{7}{5}]$ |
$[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ |
$[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 4 x^{3} + 2$ |
$[7, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.16a1.5 |
$10$ |
$x^{10} + 2 x^{7} + 4 x + 2$ |
$2$ |
$1$ |
$10$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{12}{5}]$ |
$[\frac{7}{5}]$ |
$[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ |
$[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 4 x + 2$ |
$[7, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.16a1.7 |
$10$ |
$x^{10} + 2 x^{7} + 4 x^{3} + 4 x + 2$ |
$2$ |
$1$ |
$10$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{12}{5}]$ |
$[\frac{7}{5}]$ |
$[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ |
$[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 4 x^{3} + 4 x + 2$ |
$[7, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.18a1.10 |
$10$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$18$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{14}{5}]$ |
$[\frac{9}{5}]$ |
$[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}]_{5}^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]_{5}^{4}$ |
$[\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{3} + 2$ |
$[9, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.18a1.12 |
$10$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$18$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{14}{5}]$ |
$[\frac{9}{5}]$ |
$[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}]_{5}^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]_{5}^{4}$ |
$[\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{3} + 2$ |
$[9, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.18a1.14 |
$10$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$18$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{14}{5}]$ |
$[\frac{9}{5}]$ |
$[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}]_{5}^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]_{5}^{4}$ |
$[\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 2$ |
$[9, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.18a1.16 |
$10$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$18$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{14}{5}]$ |
$[\frac{9}{5}]$ |
$[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}]_{5}^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]_{5}^{4}$ |
$[\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 2$ |
$[9, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.18a1.26 |
$10$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{3} + 4 x + 2$ |
$2$ |
$1$ |
$10$ |
$18$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{14}{5}]$ |
$[\frac{9}{5}]$ |
$[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}]_{5}^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]_{5}^{4}$ |
$[\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{3} + 4 x + 2$ |
$[9, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.18a1.28 |
$10$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{3} + 4 x + 2$ |
$2$ |
$1$ |
$10$ |
$18$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{14}{5}]$ |
$[\frac{9}{5}]$ |
$[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}]_{5}^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]_{5}^{4}$ |
$[\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{3} + 4 x + 2$ |
$[9, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.18a1.30 |
$10$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 4 x + 2$ |
$2$ |
$1$ |
$10$ |
$18$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{14}{5}]$ |
$[\frac{9}{5}]$ |
$[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}]_{5}^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]_{5}^{4}$ |
$[\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{3} + 4 x + 2$ |
$[9, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.18a1.32 |
$10$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 4 x + 2$ |
$2$ |
$1$ |
$10$ |
$18$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{14}{5}]$ |
$[\frac{9}{5}]$ |
$[\frac{14}{5}, \frac{14}{5}, \frac{14}{5}, \frac{14}{5}]_{5}^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5},\frac{9}{5}]_{5}^{4}$ |
$[\frac{14}{5},\frac{14}{5},\frac{14}{5}]^{4}$ |
$[\frac{9}{5},\frac{9}{5},\frac{9}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{3} + 4 x + 2$ |
$[9, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
