| 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 |
| 5.1.15.16a1.1 |
$15$ |
$x^{15} + 10 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$16$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}, \frac{7}{6}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6}]_{6}^{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{2} + 5$ |
$[2, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.16a1.2 |
$15$ |
$x^{15} + 15 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$16$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}, \frac{7}{6}]_{6}^{2}$ |
$[\frac{1}{6},\frac{1}{6}]_{6}^{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$[\frac{1}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{2} + 5$ |
$[2, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.18a1.1 |
$15$ |
$x^{15} + 5 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{4}$ |
$[\frac{4}{3}]^{4}$ |
$[\frac{1}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{4} + 5$ |
$[4, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 1$ |
undefined |
| 5.1.15.18a4.1 |
$15$ |
$x^{15} + 20 x^{4} + 5$ |
$5$ |
$1$ |
$15$ |
$18$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}, \frac{4}{3}]_{3}^{4}$ |
$[\frac{1}{3},\frac{1}{3}]_{3}^{4}$ |
$[\frac{4}{3}]^{4}$ |
$[\frac{1}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{4} + 5$ |
$[4, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 4$ |
undefined |
| 5.1.15.22a1.1 |
$15$ |
$x^{15} + 15 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 1$ |
undefined |
| 5.1.15.22a1.2 |
$15$ |
$x^{15} + 5 x^{9} + 15 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{9} + 15 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 1$ |
undefined |
| 5.1.15.22a1.3 |
$15$ |
$x^{15} + 10 x^{9} + 15 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{9} + 15 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 1$ |
undefined |
| 5.1.15.22a1.4 |
$15$ |
$x^{15} + 15 x^{9} + 15 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{9} + 15 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 1$ |
undefined |
| 5.1.15.22a1.5 |
$15$ |
$x^{15} + 20 x^{9} + 15 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{9} + 15 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 1$ |
undefined |
| 5.1.15.22a4.1 |
$15$ |
$x^{15} + 10 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 4$ |
undefined |
| 5.1.15.22a4.2 |
$15$ |
$x^{15} + 5 x^{9} + 10 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{9} + 10 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 4$ |
undefined |
| 5.1.15.22a4.3 |
$15$ |
$x^{15} + 10 x^{9} + 10 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 10 x^{9} + 10 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 4$ |
undefined |
| 5.1.15.22a4.4 |
$15$ |
$x^{15} + 15 x^{9} + 10 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 15 x^{9} + 10 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 4$ |
undefined |
| 5.1.15.22a4.5 |
$15$ |
$x^{15} + 20 x^{9} + 10 x^{8} + 5$ |
$5$ |
$1$ |
$15$ |
$22$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$4$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}, \frac{5}{3}]_{3}^{4}$ |
$[\frac{2}{3},\frac{2}{3}]_{3}^{4}$ |
$[\frac{5}{3}]^{4}$ |
$[\frac{2}{3}]^{4}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{9} + 10 x^{8} + 5$ |
$[8, 0]$ |
$[2, 4]$ |
$z^{10} + 3 z^5 + 3,3 z^4 + 4$ |
undefined |
| 5.1.15.28a1.1 |
$15$ |
$x^{15} + 5 x^{14} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.28a1.2 |
$15$ |
$x^{15} + 5 x^{14} + 25 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 25 x^{2} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.28a1.3 |
$15$ |
$x^{15} + 5 x^{14} + 50 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 50 x^{2} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.28a1.4 |
$15$ |
$x^{15} + 5 x^{14} + 75 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 75 x^{2} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.28a1.5 |
$15$ |
$x^{15} + 5 x^{14} + 100 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 5 x^{14} + 100 x^{2} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 1$ |
undefined |
| 5.1.15.28a1.26 |
$15$ |
$x^{15} + 20 x^{14} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.28a1.27 |
$15$ |
$x^{15} + 20 x^{14} + 25 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 25 x^{2} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.28a1.28 |
$15$ |
$x^{15} + 20 x^{14} + 50 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 50 x^{2} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.28a1.29 |
$15$ |
$x^{15} + 20 x^{14} + 75 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 75 x^{2} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
| 5.1.15.28a1.30 |
$15$ |
$x^{15} + 20 x^{14} + 100 x^{2} + 5$ |
$5$ |
$1$ |
$15$ |
$28$ |
$(C_5^2 : C_3):C_4$ (as 15T17) |
$2$ |
$6$ |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
$[\frac{13}{6}, \frac{13}{6}]_{6}^{2}$ |
$[\frac{7}{6},\frac{7}{6}]_{6}^{2}$ |
$[\frac{13}{6}]^{2}_{2}$ |
$[\frac{7}{6}]^{2}_{2}$ |
$1$ |
$t + 3$ |
$x^{15} + 20 x^{14} + 100 x^{2} + 5$ |
$[14, 0]$ |
$[2, 2]$ |
$z^{10} + 3 z^5 + 3,3 z^2 + 4$ |
undefined |
