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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
3.15.22.1	$15$	$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{8} + 3$	$[8, 0]$	$[2, 4]$
3.15.22.10	$15$	$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.11	$15$	$x^{15} + 3 x^{12} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{12} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.12	$15$	$x^{15} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{12} + 3 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.13	$15$	$x^{15} + 6 x^{12} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{12} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.14	$15$	$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.15	$15$	$x^{15} + 6 x^{10} + 6 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 6 x^{10} + 6 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$[8, 0]$	$[2, 4]$
3.15.22.16	$15$	$x^{15} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.17	$15$	$x^{15} + 3 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.18	$15$	$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{9} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.19	$15$	$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 6 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 6 x^{8} + 3$	$[8, 0]$	$[2, 4]$
3.15.22.2	$15$	$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 3$	$[8, 0]$	$[2, 4]$
3.15.22.20	$15$	$x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.21	$15$	$x^{15} + 3 x^{9} + 6 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{9} + 6 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$[8, 0]$	$[2, 4]$
3.15.22.22	$15$	$x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.23	$15$	$x^{15} + 3 x^{12} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 3 x^{12} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.24	$15$	$x^{15} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.25	$15$	$x^{15} + 3 x^{11} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{11} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.26	$15$	$x^{15} + 6 x^{11} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 6 x^{11} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.27	$15$	$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.28	$15$	$x^{15} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.29	$15$	$x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 3 x^{11} + 6 x^{9} + 3 x^{8} + 3 x^{6} + 3 x^{3} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.3	$15$	$x^{15} + 6 x^{12} + 6 x^{10} + 3 x^{9} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 6 x^{12} + 6 x^{10} + 3 x^{9} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$[8, 0]$	$[2, 4]$
3.15.22.30	$15$	$x^{15} + 3 x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 3 x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.31	$15$	$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.32	$15$	$x^{15} + 6 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.33	$15$	$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T41)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.34	$15$	$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.35	$15$	$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.36	$15$	$x^{15} + 3 x^{12} + 6 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 3 x^{12} + 6 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.4	$15$	$x^{15} + 3 x^{11} + 6 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{11} + 6 x^{8} + 3$	$[8, 0]$	$[2, 4]$
3.15.22.5	$15$	$x^{15} + 6 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 6 x^{10} + 3 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.6	$15$	$x^{15} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 3 x^{12} + 6 x^{11} + 6 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.7	$15$	$x^{15} + 3 x^{12} + 6 x^{10} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{12} + 6 x^{10} + 6 x^{8} + 3 x^{6} + 6 x^{3} + 3$	$[8, 0]$	$[2, 4]$
3.15.22.8	$15$	$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3\wr F_5$ (as 15T56)	$12$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{12}$	$t + 1$	$x^{15} + 3 x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{8} + 3$	$[8, 0]$	$[1, 4]$
3.15.22.9	$15$	$x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 3$	$3$	$15$	$1$	$22$	$C_3^4:F_5$ (as 15T42)	$4$	$5$	$[9/5]$	$[9/5, 9/5, 9/5, 9/5]_{5}^{4}$	$t + 1$	$x^{15} + 3 x^{12} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 3$	$[8, 0]$	$[2, 4]$

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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.