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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 96 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
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)	$1$	$1$	$[2, 3]$	$[2, 3]$	$t + 1$	$x^{9} + 9 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 66$	$[14, 6, 0]$	$[1, 1]$
3.9.22.10	$9$	$x^{9} + 21 x^{6} + 18 x^{5} + 75$	$3$	$9$	$1$	$22$	$D_{9}$ (as 9T3)	$2$	$1$	$[2, 3]$	$[2, 3]^{2}$	$t + 1$	$x^{9} + 21 x^{6} + 18 x^{5} + 75$	$[14, 6, 0]$	$[2, 2]$
3.9.22.11	$9$	$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 3$	$3$	$9$	$1$	$22$	$C_9:C_3$ (as 9T6)	$3$	$1$	$[2, 3]$	$[2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 3$	$[14, 6, 0]$	$[1, 1]$
3.9.22.12	$9$	$x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 21$	$3$	$9$	$1$	$22$	$C_9:C_3$ (as 9T6)	$3$	$1$	$[2, 3]$	$[2, 3]^{3}$	$t + 1$	$x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 21$	$[14, 6, 0]$	$[1, 1]$
3.9.22.13	$9$	$x^{9} + 9 x^{7} + 24 x^{6} + 18 x^{5} + 12$	$3$	$9$	$1$	$22$	$C_9:C_3$ (as 9T6)	$3$	$1$	$[2, 3]$	$[2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{7} + 24 x^{6} + 18 x^{5} + 12$	$[14, 6, 0]$	$[1, 1]$
3.9.22.14	$9$	$x^{9} + 9 x^{7} + 24 x^{6} + 18 x^{5} + 75$	$3$	$9$	$1$	$22$	$C_9:C_3$ (as 9T6)	$3$	$1$	$[2, 3]$	$[2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{7} + 24 x^{6} + 18 x^{5} + 75$	$[14, 6, 0]$	$[1, 1]$
3.9.22.15	$9$	$x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 57$	$3$	$9$	$1$	$22$	$C_9:C_3$ (as 9T6)	$3$	$1$	$[2, 3]$	$[2, 3]^{3}$	$t + 1$	$x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 57$	$[14, 6, 0]$	$[1, 1]$
3.9.22.16	$9$	$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 12$	$3$	$9$	$1$	$22$	$C_9:C_3$ (as 9T6)	$3$	$1$	$[2, 3]$	$[2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 12$	$[14, 6, 0]$	$[1, 1]$
3.9.22.17	$9$	$x^{9} + 9 x^{8} + 12 x^{6} + 18 x^{5} + 48$	$3$	$9$	$1$	$22$	$(C_9:C_3):C_2$ (as 9T10)	$6$	$1$	$[2, 3]$	$[2, 3]^{6}$	$t + 1$	$x^{9} + 9 x^{8} + 12 x^{6} + 18 x^{5} + 48$	$[14, 6, 0]$	$[2, 2]$
3.9.22.18	$9$	$x^{9} + 9 x^{8} + 3 x^{6} + 18 x^{5} + 57$	$3$	$9$	$1$	$22$	$(C_9:C_3):C_2$ (as 9T10)	$6$	$1$	$[2, 3]$	$[2, 3]^{6}$	$t + 1$	$x^{9} + 9 x^{8} + 3 x^{6} + 18 x^{5} + 57$	$[14, 6, 0]$	$[2, 2]$
3.9.22.19	$9$	$x^{9} + 18 x^{7} + 12 x^{6} + 18 x^{5} + 75$	$3$	$9$	$1$	$22$	$(C_9:C_3):C_2$ (as 9T10)	$2$	$1$	$[2, 3]$	$[2, 2, 3]^{2}$	$t + 1$	$x^{9} + 18 x^{7} + 12 x^{6} + 18 x^{5} + 75$	$[14, 6, 0]$	$[2, 2]$
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)	$1$	$1$	$[2, 3]$	$[2, 3]$	$t + 1$	$x^{9} + 9 x^{7} + 24 x^{6} + 18 x^{5} + 30$	$[14, 6, 0]$	$[1, 1]$
3.9.22.20	$9$	$x^{9} + 9 x^{7} + 3 x^{6} + 18 x^{5} + 75$	$3$	$9$	$1$	$22$	$(C_9:C_3):C_2$ (as 9T10)	$2$	$1$	$[2, 3]$	$[2, 2, 3]^{2}$	$t + 1$	$x^{9} + 9 x^{7} + 3 x^{6} + 18 x^{5} + 75$	$[14, 6, 0]$	$[2, 2]$
3.9.22.21	$9$	$x^{9} + 9 x^{8} + 9 x^{7} + 21 x^{6} + 18 x^{5} + 57$	$3$	$9$	$1$	$22$	$(C_9:C_3):C_2$ (as 9T10)	$2$	$1$	$[2, 3]$	$[2, 2, 3]^{2}$	$t + 1$	$x^{9} + 9 x^{8} + 9 x^{7} + 21 x^{6} + 18 x^{5} + 57$	$[14, 6, 0]$	$[2, 2]$
3.9.22.22	$9$	$x^{9} + 18 x^{8} + 18 x^{7} + 12 x^{6} + 18 x^{5} + 30$	$3$	$9$	$1$	$22$	$(C_9:C_3):C_2$ (as 9T10)	$2$	$1$	$[2, 3]$	$[2, 2, 3]^{2}$	$t + 1$	$x^{9} + 18 x^{8} + 18 x^{7} + 12 x^{6} + 18 x^{5} + 30$	$[14, 6, 0]$	$[2, 2]$
3.9.22.23	$9$	$x^{9} + 18 x^{7} + 3 x^{6} + 18 x^{5} + 3$	$3$	$9$	$1$	$22$	$(C_9:C_3):C_2$ (as 9T10)	$2$	$1$	$[2, 3]$	$[2, 2, 3]^{2}$	$t + 1$	$x^{9} + 18 x^{7} + 3 x^{6} + 18 x^{5} + 3$	$[14, 6, 0]$	$[2, 2]$
3.9.22.24	$9$	$x^{9} + 18 x^{8} + 9 x^{7} + 21 x^{6} + 18 x^{5} + 3$	$3$	$9$	$1$	$22$	$(C_9:C_3):C_2$ (as 9T10)	$2$	$1$	$[2, 3]$	$[2, 2, 3]^{2}$	$t + 1$	$x^{9} + 18 x^{8} + 9 x^{7} + 21 x^{6} + 18 x^{5} + 3$	$[14, 6, 0]$	$[2, 2]$
3.9.22.25	$9$	$x^{9} + 18 x^{7} + 6 x^{6} + 18 x^{5} + 3$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 18 x^{7} + 6 x^{6} + 18 x^{5} + 3$	$[14, 6, 0]$	$[1, 1]$
3.9.22.26	$9$	$x^{9} + 18 x^{7} + 6 x^{6} + 18 x^{5} + 57$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 18 x^{7} + 6 x^{6} + 18 x^{5} + 57$	$[14, 6, 0]$	$[1, 1]$
3.9.22.27	$9$	$x^{9} + 6 x^{6} + 18 x^{5} + 39$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 18 x^{5} + 39$	$[14, 6, 0]$	$[1, 1]$
3.9.22.28	$9$	$x^{9} + 9 x^{8} + 15 x^{6} + 18 x^{5} + 3$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{8} + 15 x^{6} + 18 x^{5} + 3$	$[14, 6, 0]$	$[1, 1]$
3.9.22.29	$9$	$x^{9} + 6 x^{6} + 18 x^{5} + 75$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 18 x^{5} + 75$	$[14, 6, 0]$	$[1, 1]$
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)	$1$	$1$	$[2, 3]$	$[2, 3]$	$t + 1$	$x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 12$	$[14, 6, 0]$	$[1, 1]$
3.9.22.30	$9$	$x^{9} + 18 x^{8} + 6 x^{6} + 18 x^{5} + 21$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 18 x^{8} + 6 x^{6} + 18 x^{5} + 21$	$[14, 6, 0]$	$[1, 1]$
3.9.22.31	$9$	$x^{9} + 24 x^{6} + 18 x^{5} + 18 x^{3} + 21$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 24 x^{6} + 18 x^{5} + 18 x^{3} + 21$	$[14, 6, 0]$	$[1, 1]$
3.9.22.32	$9$	$x^{9} + 18 x^{8} + 6 x^{6} + 18 x^{5} + 18 x^{3} + 39$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 18 x^{8} + 6 x^{6} + 18 x^{5} + 18 x^{3} + 39$	$[14, 6, 0]$	$[1, 1]$
3.9.22.33	$9$	$x^{9} + 9 x^{8} + 6 x^{6} + 18 x^{5} + 18 x^{3} + 21$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{8} + 6 x^{6} + 18 x^{5} + 18 x^{3} + 21$	$[14, 6, 0]$	$[1, 1]$
3.9.22.34	$9$	$x^{9} + 18 x^{7} + 24 x^{6} + 18 x^{5} + 30$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 18 x^{7} + 24 x^{6} + 18 x^{5} + 30$	$[14, 6, 0]$	$[1, 1]$
3.9.22.35	$9$	$x^{9} + 6 x^{6} + 18 x^{5} + 66$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 18 x^{5} + 66$	$[14, 6, 0]$	$[1, 1]$
3.9.22.36	$9$	$x^{9} + 6 x^{6} + 18 x^{5} + 3$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 18 x^{5} + 3$	$[14, 6, 0]$	$[1, 1]$
3.9.22.37	$9$	$x^{9} + 18 x^{8} + 6 x^{6} + 18 x^{5} + 48$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 18 x^{8} + 6 x^{6} + 18 x^{5} + 48$	$[14, 6, 0]$	$[1, 1]$
3.9.22.38	$9$	$x^{9} + 6 x^{6} + 18 x^{5} + 30$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 18 x^{5} + 30$	$[14, 6, 0]$	$[1, 1]$
3.9.22.39	$9$	$x^{9} + 24 x^{6} + 18 x^{5} + 18 x^{3} + 12$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 24 x^{6} + 18 x^{5} + 18 x^{3} + 12$	$[14, 6, 0]$	$[1, 1]$
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)	$1$	$1$	$[2, 3]$	$[2, 3]$	$t + 1$	$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 48$	$[14, 6, 0]$	$[1, 1]$
3.9.22.40	$9$	$x^{9} + 9 x^{8} + 18 x^{7} + 24 x^{6} + 18 x^{5} + 39$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{8} + 18 x^{7} + 24 x^{6} + 18 x^{5} + 39$	$[14, 6, 0]$	$[1, 1]$
3.9.22.41	$9$	$x^{9} + 9 x^{8} + 15 x^{6} + 18 x^{5} + 66$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{8} + 15 x^{6} + 18 x^{5} + 66$	$[14, 6, 0]$	$[1, 1]$
3.9.22.42	$9$	$x^{9} + 9 x^{8} + 18 x^{7} + 24 x^{6} + 18 x^{5} + 75$	$3$	$9$	$1$	$22$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{8} + 18 x^{7} + 24 x^{6} + 18 x^{5} + 75$	$[14, 6, 0]$	$[1, 1]$
3.9.22.43	$9$	$x^{9} + 18 x^{7} + 18 x^{6} + 18 x^{5} + 3$	$3$	$9$	$1$	$22$	$C_3^2 : C_6$ (as 9T11)	$1$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}$	$t + 1$	$x^{9} + 18 x^{7} + 18 x^{6} + 18 x^{5} + 3$	$[14, 9, 0]$	$[1, 1]$
3.9.22.44	$9$	$x^{9} + 18 x^{5} + 18 x^{3} + 21$	$3$	$9$	$1$	$22$	$C_3^2 : C_6$ (as 9T11)	$1$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}$	$t + 1$	$x^{9} + 18 x^{5} + 18 x^{3} + 21$	$[14, 9, 0]$	$[1, 1]$
3.9.22.45	$9$	$x^{9} + 18 x^{7} + 18 x^{5} + 21$	$3$	$9$	$1$	$22$	$C_3^2 : C_6$ (as 9T11)	$1$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}$	$t + 1$	$x^{9} + 18 x^{7} + 18 x^{5} + 21$	$[14, 9, 0]$	$[1, 1]$
3.9.22.46	$9$	$x^{9} + 18 x^{5} + 3$	$3$	$9$	$1$	$22$	$C_3^2 : C_6$ (as 9T11)	$1$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}$	$t + 1$	$x^{9} + 18 x^{5} + 3$	$[14, 9, 0]$	$[1, 1]$
3.9.22.47	$9$	$x^{9} + 18 x^{5} + 21$	$3$	$9$	$1$	$22$	$C_3^2 : C_6$ (as 9T11)	$1$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}$	$t + 1$	$x^{9} + 18 x^{5} + 21$	$[14, 9, 0]$	$[1, 1]$
3.9.22.48	$9$	$x^{9} + 9 x^{7} + 18 x^{6} + 18 x^{5} + 9 x^{3} + 3$	$3$	$9$	$1$	$22$	$C_3^2 : C_6$ (as 9T11)	$1$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}$	$t + 1$	$x^{9} + 9 x^{7} + 18 x^{6} + 18 x^{5} + 9 x^{3} + 3$	$[14, 9, 0]$	$[1, 1]$
3.9.22.49	$9$	$x^{9} + 18 x^{5} + 18 x^{3} + 3$	$3$	$9$	$1$	$22$	$C_3^2 : C_6$ (as 9T11)	$1$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}$	$t + 1$	$x^{9} + 18 x^{5} + 18 x^{3} + 3$	$[14, 9, 0]$	$[1, 1]$
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)	$1$	$1$	$[2, 3]$	$[2, 3]$	$t + 1$	$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 21$	$[14, 6, 0]$	$[1, 1]$
3.9.22.50	$9$	$x^{9} + 9 x^{7} + 9 x^{6} + 18 x^{5} + 3$	$3$	$9$	$1$	$22$	$C_3^2 : C_6$ (as 9T11)	$1$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}$	$t + 1$	$x^{9} + 9 x^{7} + 9 x^{6} + 18 x^{5} + 3$	$[14, 9, 0]$	$[1, 1]$
3.9.22.51	$9$	$x^{9} + 9 x^{8} + 18 x^{6} + 18 x^{5} + 9 x^{3} + 3$	$3$	$9$	$1$	$22$	$C_3^2 : C_6$ (as 9T11)	$1$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}$	$t + 1$	$x^{9} + 9 x^{8} + 18 x^{6} + 18 x^{5} + 9 x^{3} + 3$	$[14, 9, 0]$	$[1, 1]$
3.9.22.52	$9$	$x^{9} + 9 x^{5} + 9 x^{3} + 3$	$3$	$9$	$1$	$22$	$C_3^2 : D_{6} $ (as 9T18)	$2$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}^{2}$	$t + 1$	$x^{9} + 9 x^{5} + 9 x^{3} + 3$	$[14, 9, 0]$	$[1, 1]$
3.9.22.53	$9$	$x^{9} + 9 x^{7} + 18 x^{6} + 9 x^{5} + 3$	$3$	$9$	$1$	$22$	$C_3^2 : D_{6} $ (as 9T18)	$2$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}^{2}$	$t + 1$	$x^{9} + 9 x^{7} + 18 x^{6} + 9 x^{5} + 3$	$[14, 9, 0]$	$[1, 1]$
3.9.22.54	$9$	$x^{9} + 9 x^{5} + 3$	$3$	$9$	$1$	$22$	$C_3^2 : D_{6} $ (as 9T18)	$2$	$2$	$[5/2, 17/6]$	$[2, 5/2, 17/6]_{2}^{2}$	$t + 1$	$x^{9} + 9 x^{5} + 3$	$[14, 9, 0]$	$[1, 1]$

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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.