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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 (36 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
3.9.12.10	$9$	$x^{9} + 9 x^{8} + 45 x^{7} + 90 x^{6} + 324 x^{5} + 621 x^{4} + 594 x^{3} + 2349 x^{2} + 2943$	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + \left(3 t + 3\right) x^{2} + 9 t + 12$	$[2, 0]$	$[1]$
3.9.12.11	$9$	$x^{9} - 24 x^{8} + 324 x^{7} - 459 x^{6} + 828 x^{5} - 972 x^{4} + 540 x^{3} - 216 x^{2} + 432$	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 9 t^{2} + 9 t + 3$	$[2, 0]$	$[1]$
3.9.12.12	$9$	$x^{9} + 9 x^{8} + 45 x^{7} + 54 x^{6} + 189 x^{5} + 540 x^{4} + 297 x^{3} + 1944 x^{2} + 3834$	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + \left(3 t + 3\right) x^{2} + 9 t^{2} + 9 t + 12$	$[2, 0]$	$[1]$
3.9.12.13	$9$	$x^{9} - 6 x^{8} + 144 x^{7} + 927 x^{6} + 504 x^{5} + 4320 x^{4} + 1971 x^{3} + 11286 x^{2} + 17037$	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 18 t + 21$	$[2, 0]$	$[1]$
3.9.12.14	$9$	$x^{9} - 6 x^{8} + 144 x^{7} + 900 x^{6} + 612 x^{5} + 3024 x^{4} + 1080 x^{3} + 6264 x^{2} + 3672$	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 18 t + 12$	$[2, 0]$	$[1]$
3.9.12.15	$9$	$x^{9} - 24 x^{8} + 216 x^{7} - 27 x^{6} + 477 x^{5} + 1134 x^{4} + 1026 x^{3} + 3348 x^{2} + 6021$	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + \left(6 t^{2} + 3 t\right) x^{2} + 9 t^{2} + 18 t + 12$	$[2, 0]$	$[1]$
3.9.12.7	$9$	$x^{9} - 6 x^{8} + 36 x^{7} + 621 x^{6} + 477 x^{5} + 3996 x^{4} + 1026 x^{3} + 9504 x^{2} + 6021$	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + 9 t^{2} + 18 t + 12$	$[2, 0]$	$[1]$
3.9.12.8	$9$	$x^{9} - 24 x^{8} + 324 x^{7} - 405 x^{6} - 36 x^{5} + 4860 x^{4} + 540 x^{3} + 6912 x^{2} + 7236$	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 9 t^{2} + 9 t + 21$	$[2, 0]$	$[1]$
3.9.12.9	$9$	$x^{9} + 9 x^{8} + 45 x^{7} + 117 x^{6} + 486 x^{5} + 1026 x^{4} + 1485 x^{3} + 5994 x^{2} + 11934$	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + 2 t + 1$	$x^{3} + \left(3 t + 3\right) x^{2} + 9 t + 21$	$[2, 0]$	$[1]$
3.9.18.13	$9$	$x^{9} + 6 x^{6} + 9 x + 3$	$3$	$9$	$1$	$18$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 7/3]$	$[2, 2, 7/3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 9 x + 3$	$[10, 6, 0]$	$[1, 1]$
3.9.18.14	$9$	$x^{9} + 6 x^{6} + 9 x + 21$	$3$	$9$	$1$	$18$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 7/3]$	$[2, 2, 7/3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 9 x + 21$	$[10, 6, 0]$	$[1, 1]$
3.9.18.15	$9$	$x^{9} + 6 x^{6} + 18 x^{3} + 9 x + 21$	$3$	$9$	$1$	$18$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 7/3]$	$[2, 2, 7/3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 18 x^{3} + 9 x + 21$	$[10, 6, 0]$	$[1, 1]$
3.9.18.16	$9$	$x^{9} + 6 x^{6} + 18 x^{3} + 9 x + 3$	$3$	$9$	$1$	$18$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 7/3]$	$[2, 2, 7/3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 18 x^{3} + 9 x + 3$	$[10, 6, 0]$	$[1, 1]$
3.9.18.17	$9$	$x^{9} + 6 x^{6} + 9 x^{3} + 9 x + 21$	$3$	$9$	$1$	$18$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 7/3]$	$[2, 2, 7/3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 9 x^{3} + 9 x + 21$	$[10, 6, 0]$	$[1, 1]$
3.9.18.18	$9$	$x^{9} + 6 x^{6} + 9 x^{3} + 9 x + 12$	$3$	$9$	$1$	$18$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 7/3]$	$[2, 2, 7/3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 9 x^{3} + 9 x + 12$	$[10, 6, 0]$	$[1, 1]$
3.9.18.19	$9$	$x^{9} + 6 x^{6} + 9 x + 12$	$3$	$9$	$1$	$18$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 7/3]$	$[2, 2, 7/3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 9 x + 12$	$[10, 6, 0]$	$[1, 1]$
3.9.18.20	$9$	$x^{9} + 6 x^{6} + 18 x^{3} + 9 x + 12$	$3$	$9$	$1$	$18$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 7/3]$	$[2, 2, 7/3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 18 x^{3} + 9 x + 12$	$[10, 6, 0]$	$[1, 1]$
3.9.18.21	$9$	$x^{9} + 6 x^{6} + 9 x^{3} + 9 x + 3$	$3$	$9$	$1$	$18$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2, 7/3]$	$[2, 2, 7/3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 9 x^{3} + 9 x + 3$	$[10, 6, 0]$	$[1, 1]$
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)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 6 x^{6} + 18 x^{5} + 75$	$[14, 6, 0]$	$[1, 1]$
3.9.22.30	$9$	$x^{9} + 18 x^{8} + 6 x^{6} + 18 x^{5} + 21$	$3$	$9$	$1$	$22$	$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)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 24 x^{6} + 18 x^{5} + 18 x^{3} + 12$	$[14, 6, 0]$	$[1, 1]$
3.9.22.40	$9$	$x^{9} + 9 x^{8} + 18 x^{7} + 24 x^{6} + 18 x^{5} + 39$	$3$	$9$	$1$	$22$	$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)	$3$	$1$	$[2, 3]$	$[2, 2, 3]^{3}$	$t + 1$	$x^{9} + 9 x^{8} + 18 x^{7} + 24 x^{6} + 18 x^{5} + 75$	$[14, 6, 0]$	$[1, 1]$

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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.