| 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 |
| 7.18.1.0a1.1 |
$18$ |
$x^{18} + x^{12} + 2 x^{11} + 6 x^{10} + x^{9} + 6 x^{8} + 5 x^{7} + x^{6} + 3 x^{5} + 6 x^{2} + 2 x + 3$ |
$7$ |
$18$ |
$1$ |
$0$ |
$C_{18}$ (as 18T1) |
$18$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{18}$ |
$[\ ]^{18}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{18} + t^{12} + 2 t^{11} + 6 t^{10} + t^{9} + 6 t^{8} + 5 t^{7} + t^{6} + 3 t^{5} + 6 t^{2} + 2 t + 3$ |
$x - 7$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 7.9.2.9a1.1 |
$18$ |
$( x^{9} + 6 x^{4} + x^{3} + 6 x + 4 )^{2} + 7 x$ |
$7$ |
$9$ |
$2$ |
$9$ |
$C_{18}$ (as 18T1) |
$9$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{9}$ |
$[\ ]_{2}^{9}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{9} + 6 t^{4} + t^{3} + 6 t + 4$ |
$x^{2} + 7 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 7.9.2.9a1.2 |
$18$ |
$( x^{9} + 6 x^{4} + x^{3} + 6 x + 4 )^{2} + 7$ |
$7$ |
$9$ |
$2$ |
$9$ |
$C_{18}$ (as 18T1) |
$9$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{9}$ |
$[\ ]_{2}^{9}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{9} + 6 t^{4} + t^{3} + 6 t + 4$ |
$x^{2} + 7$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 7.6.3.12a1.1 |
$18$ |
$( x^{6} + x^{4} + 5 x^{3} + 4 x^{2} + 6 x + 3 )^{3} + 7 x^{2}$ |
$7$ |
$6$ |
$3$ |
$12$ |
$C_{18}$ (as 18T1) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{6} + t^{4} + 5 t^{3} + 4 t^{2} + 6 t + 3$ |
$x^{3} + 7 t^{2}$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 7.6.3.12a1.2 |
$18$ |
$( x^{6} + x^{4} + 5 x^{3} + 4 x^{2} + 6 x + 3 )^{3} + 7 x$ |
$7$ |
$6$ |
$3$ |
$12$ |
$C_{18}$ (as 18T1) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{6} + t^{4} + 5 t^{3} + 4 t^{2} + 6 t + 3$ |
$x^{3} + 7 t$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 7.6.3.12a1.3 |
$18$ |
$( x^{6} + x^{4} + 5 x^{3} + 4 x^{2} + 6 x + 3 )^{3} + 7$ |
$7$ |
$6$ |
$3$ |
$12$ |
$C_6 \times C_3$ (as 18T2) |
$6$ |
$3$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{3}^{6}$ |
$[\ ]_{3}^{6}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{6} + t^{4} + 5 t^{3} + 4 t^{2} + 6 t + 3$ |
$x^{3} + 7$ |
$[0]$ |
$[1]$ |
$z^2 + 3 z + 3$ |
undefined |
| 7.3.6.15a1.1 |
$18$ |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7 x^{2}$ |
$7$ |
$3$ |
$6$ |
$15$ |
$C_{18}$ (as 18T1) |
$3$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{6} + 7 t^{2}$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
| 7.3.6.15a1.2 |
$18$ |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7 x$ |
$7$ |
$3$ |
$6$ |
$15$ |
$C_{18}$ (as 18T1) |
$3$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{6} + 7 t$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
| 7.3.6.15a1.3 |
$18$ |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7$ |
$7$ |
$3$ |
$6$ |
$15$ |
$C_6 \times C_3$ (as 18T2) |
$3$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{6} + 7$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
$[1]$ |
| 7.3.6.15a1.4 |
$18$ |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7 x^{2} + 21$ |
$7$ |
$3$ |
$6$ |
$15$ |
$C_6 \times C_3$ (as 18T2) |
$3$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{6} + 7 t^{2} + 21$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
| 7.3.6.15a1.5 |
$18$ |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7 x^{2} + 21 x + 21$ |
$7$ |
$3$ |
$6$ |
$15$ |
$C_{18}$ (as 18T1) |
$3$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{6} + 7 t^{2} + 21 t + 21$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
| 7.3.6.15a1.6 |
$18$ |
$( x^{3} + 6 x^{2} + 4 )^{6} + 28 x^{2} + 21 x + 21$ |
$7$ |
$3$ |
$6$ |
$15$ |
$C_{18}$ (as 18T1) |
$3$ |
$6$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$18$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{6} + 28 t^{2} + 21 t + 21$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
| 7.2.9.16a1.1 |
$18$ |
$( x^{2} + 6 x + 3 )^{9} + 7 x$ |
$7$ |
$2$ |
$9$ |
$16$ |
$C_9:C_6$ (as 18T14) |
$6$ |
$9$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{9}^{6}$ |
$[\ ]_{9}^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t^{2} + 6 t + 3$ |
$x^{9} + 7 t$ |
$[0]$ |
$[3]$ |
$z^8 + 2 z^7 + z^6 + z + 2$ |
undefined |
| 7.2.9.16a1.2 |
$18$ |
$( x^{2} + 6 x + 3 )^{9} + 7$ |
$7$ |
$2$ |
$9$ |
$16$ |
$C_9:C_6$ (as 18T14) |
$6$ |
$9$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{9}^{6}$ |
$[\ ]_{9}^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t^{2} + 6 t + 3$ |
$x^{9} + 7$ |
$[0]$ |
$[3]$ |
$z^8 + 2 z^7 + z^6 + z + 2$ |
undefined |
| 7.2.9.16a1.3 |
$18$ |
$( x^{2} + 6 x + 3 )^{9} + 7 x + 28$ |
$7$ |
$2$ |
$9$ |
$16$ |
$C_9:C_6$ (as 18T14) |
$6$ |
$9$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{9}^{6}$ |
$[\ ]_{9}^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t^{2} + 6 t + 3$ |
$x^{9} + 7 t + 28$ |
$[0]$ |
$[3]$ |
$z^8 + 2 z^7 + z^6 + z + 2$ |
undefined |
| 7.1.18.17a1.1 |
$18$ |
$x^{18} + 7$ |
$7$ |
$1$ |
$18$ |
$17$ |
$C_9:C_6$ (as 18T14) |
$3$ |
$18$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{18}^{3}$ |
$[\ ]_{18}^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t + 4$ |
$x^{18} + 7$ |
$[0]$ |
$[3]$ |
$z^{17} + 4 z^{16} + 6 z^{15} + 4 z^{14} + z^{13} + 2 z^{10} + z^9 + 5 z^8 + z^7 + 2 z^6 + z^3 + 4 z^2 + 6 z + 4$ |
$[3]$ |
| 7.1.18.17a1.2 |
$18$ |
$x^{18} + 14$ |
$7$ |
$1$ |
$18$ |
$17$ |
$C_9:C_6$ (as 18T14) |
$3$ |
$18$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{18}^{3}$ |
$[\ ]_{18}^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t + 4$ |
$x^{18} + 14$ |
$[0]$ |
$[3]$ |
$z^{17} + 4 z^{16} + 6 z^{15} + 4 z^{14} + z^{13} + 2 z^{10} + z^9 + 5 z^8 + z^7 + 2 z^6 + z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.1.18.17a1.3 |
$18$ |
$x^{18} + 21$ |
$7$ |
$1$ |
$18$ |
$17$ |
$C_9:C_6$ (as 18T14) |
$3$ |
$18$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{18}^{3}$ |
$[\ ]_{18}^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t + 4$ |
$x^{18} + 21$ |
$[0]$ |
$[3]$ |
$z^{17} + 4 z^{16} + 6 z^{15} + 4 z^{14} + z^{13} + 2 z^{10} + z^9 + 5 z^8 + z^7 + 2 z^6 + z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.1.18.17a1.4 |
$18$ |
$x^{18} + 28$ |
$7$ |
$1$ |
$18$ |
$17$ |
$C_9:C_6$ (as 18T14) |
$3$ |
$18$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{18}^{3}$ |
$[\ ]_{18}^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t + 4$ |
$x^{18} + 28$ |
$[0]$ |
$[3]$ |
$z^{17} + 4 z^{16} + 6 z^{15} + 4 z^{14} + z^{13} + 2 z^{10} + z^9 + 5 z^8 + z^7 + 2 z^6 + z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.1.18.17a1.5 |
$18$ |
$x^{18} + 35$ |
$7$ |
$1$ |
$18$ |
$17$ |
$C_9:C_6$ (as 18T14) |
$3$ |
$18$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{18}^{3}$ |
$[\ ]_{18}^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t + 4$ |
$x^{18} + 35$ |
$[0]$ |
$[3]$ |
$z^{17} + 4 z^{16} + 6 z^{15} + 4 z^{14} + z^{13} + 2 z^{10} + z^9 + 5 z^8 + z^7 + 2 z^6 + z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.1.18.17a1.6 |
$18$ |
$x^{18} + 42$ |
$7$ |
$1$ |
$18$ |
$17$ |
$C_9:C_6$ (as 18T14) |
$3$ |
$18$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{18}^{3}$ |
$[\ ]_{18}^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t + 4$ |
$x^{18} + 42$ |
$[0]$ |
$[3]$ |
$z^{17} + 4 z^{16} + 6 z^{15} + 4 z^{14} + z^{13} + 2 z^{10} + z^9 + 5 z^8 + z^7 + 2 z^6 + z^3 + 4 z^2 + 6 z + 4$ |
undefined |
