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

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.