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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
Ramification index Discriminant exponent Inertia subgroup Galois tame degree Indices
Residue field degree Top slope Wild Visible Wild inertia subgroup
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Results (1-50 of 171 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.9.0.1 $x^{9} + x^{4} + 1$ $2$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + t^{4} + 1$ $x - 2$
3.9.0.1 $x^{9} + 2 x^{3} + 2 x^{2} + x + 1$ $3$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 2 t^{3} + 2 t^{2} + t + 1$ $x - 3$
3.9.12.2 $x^{9} + 18 x^{8} + 108 x^{7} + 243 x^{6} + 324 x^{5} + 972 x^{4} + 1269 x^{3} + 7614 x^{2} + 15984$ $3$ $3$ $3$ $12$ $C_9$ (as 9T1) $[2]$ $[2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + 6 x^{2} + 9 t^{2} + 18 t + 21$
3.9.12.3 $x^{9} + 18 x^{8} + 108 x^{7} + 153 x^{6} - 756 x^{5} - 2268 x^{4} + 891 x^{3} + 5346 x^{2} + 9099$ $3$ $3$ $3$ $12$ $C_9$ (as 9T1) $[2]$ $[2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + 6 x^{2} + 18 t^{2} + 3$
3.9.22.1 $x^{9} + 9 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 66$ $3$ $9$ $1$ $22$ $C_9$ (as 9T1) $[2, 3]$ $[2, 3]$ $t + 1$ $x^{9} + 9 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 66$
3.9.22.2 $x^{9} + 9 x^{7} + 24 x^{6} + 18 x^{5} + 30$ $3$ $9$ $1$ $22$ $C_9$ (as 9T1) $[2, 3]$ $[2, 3]$ $t + 1$ $x^{9} + 9 x^{7} + 24 x^{6} + 18 x^{5} + 30$
3.9.22.3 $x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 12$ $3$ $9$ $1$ $22$ $C_9$ (as 9T1) $[2, 3]$ $[2, 3]$ $t + 1$ $x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 12$
3.9.22.4 $x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 48$ $3$ $9$ $1$ $22$ $C_9$ (as 9T1) $[2, 3]$ $[2, 3]$ $t + 1$ $x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 48$
3.9.22.5 $x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 21$ $3$ $9$ $1$ $22$ $C_9$ (as 9T1) $[2, 3]$ $[2, 3]$ $t + 1$ $x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 21$
3.9.22.6 $x^{9} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 57$ $3$ $9$ $1$ $22$ $C_9$ (as 9T1) $[2, 3]$ $[2, 3]$ $t + 1$ $x^{9} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 57$
3.9.22.7 $x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 39$ $3$ $9$ $1$ $22$ $C_9$ (as 9T1) $[2, 3]$ $[2, 3]$ $t + 1$ $x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 39$
3.9.22.8 $x^{9} + 24 x^{6} + 18 x^{5} + 9 x^{3} + 3$ $3$ $9$ $1$ $22$ $C_9$ (as 9T1) $[2, 3]$ $[2, 3]$ $t + 1$ $x^{9} + 24 x^{6} + 18 x^{5} + 9 x^{3} + 3$
3.9.22.9 $x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 75$ $3$ $9$ $1$ $22$ $C_9$ (as 9T1) $[2, 3]$ $[2, 3]$ $t + 1$ $x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 75$
5.9.0.1 $x^{9} + 2 x^{3} + x + 3$ $5$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 2 t^{3} + t + 3$ $x - 5$
7.9.0.1 $x^{9} + 6 x^{4} + x^{3} + 6 x + 4$ $7$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 6 t^{4} + t^{3} + 6 t + 4$ $x - 7$
7.9.6.2 $x^{9} + 252 x^{6} - 2352 x^{3} + 5488$ $7$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 6 t^{2} + 4$ $x^{3} + 7 t^{2}$
7.9.6.3 $x^{9} - 42 x^{6} - 1372$ $7$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 6 t^{2} + 4$ $x^{3} + 7 t$
11.9.0.1 $x^{9} + 9 x^{2} + 8 x + 9$ $11$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 9 t^{2} + 8 t + 9$ $x - 11$
13.9.0.1 $x^{9} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 12 x + 11$ $13$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 12 t^{4} + 8 t^{3} + 12 t^{2} + 12 t + 11$ $x - 13$
13.9.6.2 $x^{9} - 52 x^{6} + 676 x^{3} + 265837$ $13$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 2 t + 11$ $x^{3} + 13 t^{2}$
13.9.6.3 $x^{9} + 338 x^{3} - 24167$ $13$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 2 t + 11$ $x^{3} + 13 t$
17.9.0.1 $x^{9} + 7 x^{2} + 8 x + 14$ $17$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 7 t^{2} + 8 t + 14$ $x - 17$
19.9.0.1 $x^{9} + 11 x^{3} + 14 x^{2} + 16 x + 17$ $19$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 11 t^{3} + 14 t^{2} + 16 t + 17$ $x - 19$
19.9.6.1 $x^{9} + 1444 x^{3} - 116603$ $19$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 4 t + 17$ $x^{3} + 19 t$
19.9.6.3 $x^{9} - 152 x^{6} + 5776 x^{3} + 1982251$ $19$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 4 t + 17$ $x^{3} + 19 t^{2}$
19.9.8.1 $x^{9} + 76$ $19$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 17$ $x^{9} + 76$
19.9.8.2 $x^{9} + 57$ $19$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 17$ $x^{9} + 57$
19.9.8.3 $x^{9} + 152$ $19$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 17$ $x^{9} + 152$
19.9.8.4 $x^{9} + 114$ $19$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 17$ $x^{9} + 114$
19.9.8.5 $x^{9} + 38$ $19$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 17$ $x^{9} + 38$
19.9.8.6 $x^{9} + 133$ $19$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 17$ $x^{9} + 133$
19.9.8.7 $x^{9} + 95$ $19$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 17$ $x^{9} + 95$
19.9.8.8 $x^{9} + 19$ $19$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 17$ $x^{9} + 19$
19.9.8.9 $x^{9} + 171$ $19$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 17$ $x^{9} + 171$
23.9.0.1 $x^{9} + 3 x^{3} + 8 x^{2} + 9 x + 18$ $23$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 3 t^{3} + 8 t^{2} + 9 t + 18$ $x - 23$
29.9.0.1 $x^{9} + 4 x^{3} + 22 x^{2} + 22 x + 27$ $29$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 4 t^{3} + 22 t^{2} + 22 t + 27$ $x - 29$
31.9.0.1 $x^{9} + 4 x^{3} + 20 x^{2} + 29 x + 28$ $31$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 4 t^{3} + 20 t^{2} + 29 t + 28$ $x - 31$
31.9.6.2 $x^{9} - 62 x^{6} + 961 x^{3} + 23356144$ $31$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + t + 28$ $x^{3} + 31 t^{2}$
31.9.6.3 $x^{9} + 961 x^{3} - 834148$ $31$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + t + 28$ $x^{3} + 31 t$
37.9.0.1 $x^{9} + 6 x^{3} + 20 x^{2} + 32 x + 35$ $37$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$ $t^{9} + 6 t^{3} + 20 t^{2} + 32 t + 35$ $x - 37$
37.9.6.2 $x^{9} + 8214 x^{3} - 1772855$ $37$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 6 t + 35$ $x^{3} + 37 t$
37.9.6.3 $x^{9} - 444 x^{6} + 49284 x^{3} + 62049925$ $37$ $3$ $3$ $6$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{3}^{3}$ $t^{3} + 6 t + 35$ $x^{3} + 37 t^{2}$
37.9.8.1 $x^{9} + 37$ $37$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 35$ $x^{9} + 37$
37.9.8.2 $x^{9} + 74$ $37$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 35$ $x^{9} + 74$
37.9.8.3 $x^{9} + 148$ $37$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 35$ $x^{9} + 148$
37.9.8.4 $x^{9} + 296$ $37$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 35$ $x^{9} + 296$
37.9.8.5 $x^{9} + 555$ $37$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 35$ $x^{9} + 555$
37.9.8.6 $x^{9} + 185$ $37$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 35$ $x^{9} + 185$
37.9.8.7 $x^{9} + 370$ $37$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 35$ $x^{9} + 370$
37.9.8.8 $x^{9} + 333$ $37$ $9$ $1$ $8$ $C_9$ (as 9T1) $[\ ]$ $[\ ]_{9}$ $t + 35$ $x^{9} + 333$
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