| 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 |
| 13.1.13.14a1.1 |
$13$ |
$x^{13} + 26 x^{2} + 13$ |
$13$ |
$1$ |
$13$ |
$14$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 26 x^{2} + 13$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 9$ |
undefined |
| 13.1.13.14a1.2 |
$13$ |
$x^{13} + 65 x^{2} + 13$ |
$13$ |
$1$ |
$13$ |
$14$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 65 x^{2} + 13$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 3$ |
undefined |
| 13.1.13.14a1.3 |
$13$ |
$x^{13} + 78 x^{2} + 13$ |
$13$ |
$1$ |
$13$ |
$14$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 78 x^{2} + 13$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 1$ |
undefined |
| 13.1.13.14a1.4 |
$13$ |
$x^{13} + 91 x^{2} + 13$ |
$13$ |
$1$ |
$13$ |
$14$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 91 x^{2} + 13$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 12$ |
undefined |
| 13.1.13.14a1.5 |
$13$ |
$x^{13} + 104 x^{2} + 13$ |
$13$ |
$1$ |
$13$ |
$14$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 104 x^{2} + 13$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 10$ |
undefined |
| 13.1.13.14a1.6 |
$13$ |
$x^{13} + 143 x^{2} + 13$ |
$13$ |
$1$ |
$13$ |
$14$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
$[\frac{7}{6}]_{6}$ |
$[\frac{1}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 143 x^{2} + 13$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 4$ |
undefined |
| 13.1.13.16a1.1 |
$13$ |
$x^{13} + 13 x^{4} + 13$ |
$13$ |
$1$ |
$13$ |
$16$ |
$C_{13}:C_6$ (as 13T5) |
$2$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 11$ |
$x^{13} + 13 x^{4} + 13$ |
$[4, 0]$ |
$[2]$ |
$z^4 + 9$ |
undefined |
| 13.1.13.16a1.2 |
$13$ |
$x^{13} + 39 x^{4} + 13$ |
$13$ |
$1$ |
$13$ |
$16$ |
$C_{13}:C_6$ (as 13T5) |
$2$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 11$ |
$x^{13} + 39 x^{4} + 13$ |
$[4, 0]$ |
$[2]$ |
$z^4 + 1$ |
undefined |
| 13.1.13.16a1.3 |
$13$ |
$x^{13} + 117 x^{4} + 13$ |
$13$ |
$1$ |
$13$ |
$16$ |
$C_{13}:C_6$ (as 13T5) |
$2$ |
$3$ |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
$[\frac{4}{3}]_{3}^{2}$ |
$[\frac{1}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 11$ |
$x^{13} + 117 x^{4} + 13$ |
$[4, 0]$ |
$[2]$ |
$z^4 + 3$ |
undefined |
| 13.1.13.18a3.1 |
$13$ |
$x^{13} + 78 x^{6} + 13$ |
$13$ |
$1$ |
$13$ |
$18$ |
$C_{13}:C_6$ (as 13T5) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 11$ |
$x^{13} + 78 x^{6} + 13$ |
$[6, 0]$ |
$[3]$ |
$z^6 + 3$ |
undefined |
| 13.1.13.18a3.2 |
$13$ |
$x^{13} + 91 x^{6} + 13$ |
$13$ |
$1$ |
$13$ |
$18$ |
$C_{13}:C_6$ (as 13T5) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 11$ |
$x^{13} + 91 x^{6} + 13$ |
$[6, 0]$ |
$[3]$ |
$z^6 + 10$ |
undefined |
| 13.1.13.18a4.1 |
$13$ |
$x^{13} + 65 x^{6} + 13$ |
$13$ |
$1$ |
$13$ |
$18$ |
$C_{13}:C_6$ (as 13T5) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 11$ |
$x^{13} + 65 x^{6} + 13$ |
$[6, 0]$ |
$[3]$ |
$z^6 + 9$ |
undefined |
| 13.1.13.18a4.2 |
$13$ |
$x^{13} + 104 x^{6} + 13$ |
$13$ |
$1$ |
$13$ |
$18$ |
$C_{13}:C_6$ (as 13T5) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 11$ |
$x^{13} + 104 x^{6} + 13$ |
$[6, 0]$ |
$[3]$ |
$z^6 + 4$ |
undefined |
| 13.1.13.20a1.1 |
$13$ |
$x^{13} + 91 x^{8} + 13$ |
$13$ |
$1$ |
$13$ |
$20$ |
$C_{13}:C_6$ (as 13T5) |
$2$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}]_{3}^{2}$ |
$[\frac{2}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 11$ |
$x^{13} + 91 x^{8} + 13$ |
$[8, 0]$ |
$[2]$ |
$z^4 + 9$ |
undefined |
| 13.1.13.20a1.2 |
$13$ |
$x^{13} + 104 x^{8} + 13$ |
$13$ |
$1$ |
$13$ |
$20$ |
$C_{13}:C_6$ (as 13T5) |
$2$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}]_{3}^{2}$ |
$[\frac{2}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 11$ |
$x^{13} + 104 x^{8} + 13$ |
$[8, 0]$ |
$[2]$ |
$z^4 + 1$ |
undefined |
| 13.1.13.20a1.3 |
$13$ |
$x^{13} + 143 x^{8} + 13$ |
$13$ |
$1$ |
$13$ |
$20$ |
$C_{13}:C_6$ (as 13T5) |
$2$ |
$3$ |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
$[\frac{5}{3}]_{3}^{2}$ |
$[\frac{2}{3}]_{3}^{2}$ |
$[\ ]^{2}_{3}$ |
$[\ ]^{2}_{3}$ |
$1$ |
$t + 11$ |
$x^{13} + 143 x^{8} + 13$ |
$[8, 0]$ |
$[2]$ |
$z^4 + 3$ |
undefined |
| 13.1.13.22a1.1 |
$13$ |
$x^{13} + 13 x^{10} + 13$ |
$13$ |
$1$ |
$13$ |
$22$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 13 x^{10} + 13$ |
$[10, 0]$ |
$[1]$ |
$z^2 + 3$ |
undefined |
| 13.1.13.22a1.2 |
$13$ |
$x^{13} + 39 x^{10} + 13$ |
$13$ |
$1$ |
$13$ |
$22$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 39 x^{10} + 13$ |
$[10, 0]$ |
$[1]$ |
$z^2 + 9$ |
undefined |
| 13.1.13.22a1.3 |
$13$ |
$x^{13} + 52 x^{10} + 13$ |
$13$ |
$1$ |
$13$ |
$22$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 52 x^{10} + 13$ |
$[10, 0]$ |
$[1]$ |
$z^2 + 12$ |
undefined |
| 13.1.13.22a1.4 |
$13$ |
$x^{13} + 117 x^{10} + 13$ |
$13$ |
$1$ |
$13$ |
$22$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 117 x^{10} + 13$ |
$[10, 0]$ |
$[1]$ |
$z^2 + 1$ |
undefined |
| 13.1.13.22a1.5 |
$13$ |
$x^{13} + 130 x^{10} + 13$ |
$13$ |
$1$ |
$13$ |
$22$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 130 x^{10} + 13$ |
$[10, 0]$ |
$[1]$ |
$z^2 + 4$ |
undefined |
| 13.1.13.22a1.6 |
$13$ |
$x^{13} + 156 x^{10} + 13$ |
$13$ |
$1$ |
$13$ |
$22$ |
$C_{13}:C_6$ (as 13T5) |
$1$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$[\ ]_{6}$ |
$[\ ]_{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 156 x^{10} + 13$ |
$[10, 0]$ |
$[1]$ |
$z^2 + 10$ |
undefined |
| 13.1.13.24a3.1 |
$13$ |
$x^{13} + 39 x^{12} + 13$ |
$13$ |
$1$ |
$13$ |
$24$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{6}$ |
$[1]^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 39 x^{12} + 13$ |
$[12, 0]$ |
$[6]$ |
$z^{12} + 3$ |
undefined |
| 13.1.13.24a9.1 |
$13$ |
$x^{13} + 117 x^{12} + 13$ |
$13$ |
$1$ |
$13$ |
$24$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{6}$ |
$[1]^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 11$ |
$x^{13} + 117 x^{12} + 13$ |
$[12, 0]$ |
$[6]$ |
$z^{12} + 9$ |
undefined |
| 17.1.13.12a1.1 |
$13$ |
$x^{13} + 17$ |
$17$ |
$1$ |
$13$ |
$12$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$13$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{13}^{6}$ |
$[\ ]_{13}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 14$ |
$x^{13} + 17$ |
$[0]$ |
$[6]$ |
$z^{12} + 13 z^{11} + 10 z^{10} + 14 z^9 + z^8 + 12 z^7 + 16 z^6 + 16 z^5 + 12 z^4 + z^3 + 14 z^2 + 10 z + 13$ |
undefined |
| 23.1.13.12a1.1 |
$13$ |
$x^{13} + 23$ |
$23$ |
$1$ |
$13$ |
$12$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$13$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{13}^{6}$ |
$[\ ]_{13}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 18$ |
$x^{13} + 23$ |
$[0]$ |
$[6]$ |
$z^{12} + 13 z^{11} + 9 z^{10} + 10 z^9 + 2 z^8 + 22 z^7 + 14 z^6 + 14 z^5 + 22 z^4 + 2 z^3 + 10 z^2 + 9 z + 13$ |
undefined |
| 43.1.13.12a1.1 |
$13$ |
$x^{13} + 43$ |
$43$ |
$1$ |
$13$ |
$12$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$13$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{13}^{6}$ |
$[\ ]_{13}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 40$ |
$x^{13} + 43$ |
$[0]$ |
$[6]$ |
$z^{12} + 13 z^{11} + 35 z^{10} + 28 z^9 + 27 z^8 + 40 z^7 + 39 z^6 + 39 z^5 + 40 z^4 + 27 z^3 + 28 z^2 + 35 z + 13$ |
undefined |
| 101.1.13.12a1.1 |
$13$ |
$x^{13} + 101$ |
$101$ |
$1$ |
$13$ |
$12$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$13$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{13}^{6}$ |
$[\ ]_{13}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 99$ |
$x^{13} + 101$ |
$[0]$ |
$[6]$ |
$z^{12} + 13 z^{11} + 78 z^{10} + 84 z^9 + 8 z^8 + 75 z^7 + 100 z^6 + 100 z^5 + 75 z^4 + 8 z^3 + 84 z^2 + 78 z + 13$ |
undefined |
| 127.1.13.12a1.1 |
$13$ |
$x^{13} + 127$ |
$127$ |
$1$ |
$13$ |
$12$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$13$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{13}^{6}$ |
$[\ ]_{13}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 124$ |
$x^{13} + 127$ |
$[0]$ |
$[6]$ |
$z^{12} + 13 z^{11} + 78 z^{10} + 32 z^9 + 80 z^8 + 17 z^7 + 65 z^6 + 65 z^5 + 17 z^4 + 80 z^3 + 32 z^2 + 78 z + 13$ |
undefined |
| 173.1.13.12a1.1 |
$13$ |
$x^{13} + 173$ |
$173$ |
$1$ |
$13$ |
$12$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$13$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{13}^{6}$ |
$[\ ]_{13}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 171$ |
$x^{13} + 173$ |
$[0]$ |
$[6]$ |
$z^{12} + 13 z^{11} + 78 z^{10} + 113 z^9 + 23 z^8 + 76 z^7 + 159 z^6 + 159 z^5 + 76 z^4 + 23 z^3 + 113 z^2 + 78 z + 13$ |
undefined |
| 179.1.13.12a1.1 |
$13$ |
$x^{13} + 179$ |
$179$ |
$1$ |
$13$ |
$12$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$13$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{13}^{6}$ |
$[\ ]_{13}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 177$ |
$x^{13} + 179$ |
$[0]$ |
$[6]$ |
$z^{12} + 13 z^{11} + 78 z^{10} + 107 z^9 + 178 z^8 + 34 z^7 + 105 z^6 + 105 z^5 + 34 z^4 + 178 z^3 + 107 z^2 + 78 z + 13$ |
undefined |
| 199.1.13.12a1.1 |
$13$ |
$x^{13} + 199$ |
$199$ |
$1$ |
$13$ |
$12$ |
$C_{13}:C_6$ (as 13T5) |
$6$ |
$13$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{13}^{6}$ |
$[\ ]_{13}^{6}$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$1$ |
$t + 196$ |
$x^{13} + 199$ |
$[0]$ |
$[6]$ |
$z^{12} + 13 z^{11} + 78 z^{10} + 87 z^9 + 118 z^8 + 93 z^7 + 124 z^6 + 124 z^5 + 93 z^4 + 118 z^3 + 87 z^2 + 78 z + 13$ |
undefined |
