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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 (32 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
2.10.18.1	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.10	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.11	$10$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.12	$10$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.13	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.14	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.15	$10$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.16	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.17	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.18	$10$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{4} + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{4} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.19	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.2	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.20	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.21	$10$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{4} + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{5} + 4 x^{4} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.22	$10$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{4} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.23	$10$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.24	$10$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 2 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.25	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.26	$10$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{5} + 4 x^{4} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.27	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.28	$10$	$x^{10} + 2 x^{9} + 4 x^{5} + 4 x^{4} + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{5} + 4 x^{4} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.29	$10$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{4} + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{4} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.3	$10$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.30	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.31	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{3} + 4 x^{2} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.32	$10$	$x^{10} + 2 x^{9} + 4 x^{4} + 2$	$2$	$10$	$1$	$18$	$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29)	$4$	$5$	$[14/5]$	$[2, 14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{4} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.4	$10$	$x^{10} + 2 x^{9} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.5	$10$	$x^{10} + 2 x^{9} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{6} + 4 x^{5} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.6	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.7	$10$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{7} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$
2.10.18.8	$10$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T24)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 6 x^{8} + 4 x^{6} + 4 x^{5} + 4 x + 2$	$[9, 0]$	$[1, 4]$
2.10.18.9	$10$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$2$	$10$	$1$	$18$	$(C_2^4 : C_5):C_4$ (as 10T25)	$4$	$5$	$[14/5]$	$[14/5, 14/5, 14/5, 14/5]_{5}^{4}$	$t + 1$	$x^{10} + 2 x^{9} + 4 x^{8} + 4 x^{6} + 4 x^{4} + 4 x^{3} + 2$	$[9, 0]$	$[1, 4]$

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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.