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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 444 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
3.12.12.29	$12$	$x^{12} + 3 x + 3$	$3$	$12$	$1$	$12$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[9/8]$	$[9/8, 9/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x + 3$	$[1, 0]$	$[1, 2]$
3.12.12.30	$12$	$x^{12} + 3 x^{2} + 3 x + 6$	$3$	$12$	$1$	$12$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[9/8]$	$[9/8, 9/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{2} + 3 x + 6$	$[1, 0]$	$[1, 2]$
3.12.13.1	$12$	$x^{12} + 3 x^{2} + 3$	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{2} + 3$	$[2, 0]$	$[2, 2]$
3.12.13.2	$12$	$x^{12} + 3 x^{3} + 6 x^{2} + 3$	$3$	$12$	$1$	$13$	$S_3^2:C_6$ (as 12T121)	$6$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{6}$	$t + 1$	$x^{12} + 3 x^{3} + 6 x^{2} + 3$	$[2, 0]$	$[1, 2]$
3.12.13.3	$12$	$x^{12} + 3 x^{3} + 3 x^{2} + 6$	$3$	$12$	$1$	$13$	$S_3^2:C_6$ (as 12T121)	$6$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{6}$	$t + 1$	$x^{12} + 3 x^{3} + 3 x^{2} + 6$	$[2, 0]$	$[1, 2]$
3.12.13.4	$12$	$x^{12} + 6 x^{2} + 6$	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T36)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{2} + 6$	$[2, 0]$	$[2, 2]$
3.12.13.5	$12$	$x^{12} + 6 x^{2} + 3$	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T35)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{2} + 3$	$[2, 0]$	$[1, 2]$
3.12.13.6	$12$	$x^{12} + 3 x^{2} + 6$	$3$	$12$	$1$	$13$	$\SOPlus(4,2)$ (as 12T35)	$2$	$4$	$[5/4]$	$[5/4, 5/4]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{2} + 6$	$[2, 0]$	$[1, 2]$
3.12.15.1	$12$	$x^{12} + 3 x^{4} + 3$	$3$	$12$	$1$	$15$	$(C_6\times C_2):C_2$ (as 12T15)	$2$	$4$	$[3/2]$	$[3/2]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{4} + 3$	$[4, 0]$	$[1, 2]$
3.12.15.10	$12$	$x^{12} + 3 x^{4} + 3 x^{3} + 6$	$3$	$12$	$1$	$15$	$S_3^2:S_3$ (as 12T120)	$2$	$4$	$[3/2]$	$[5/4, 5/4, 3/2]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{4} + 3 x^{3} + 6$	$[4, 0]$	$[2, 2]$
3.12.15.11	$12$	$x^{12} + 3 x^{6} + 6 x^{4} + 6$	$3$	$12$	$1$	$15$	$C_6\wr C_2$ (as 12T42)	$6$	$4$	$[3/2]$	$[3/2]_{4}^{6}$	$t + 1$	$x^{12} + 3 x^{6} + 6 x^{4} + 6$	$[4, 0]$	$[1, 2]$
3.12.15.12	$12$	$x^{12} + 6 x^{6} + 6 x^{4} + 3$	$3$	$12$	$1$	$15$	$(C_6\times C_2):C_2$ (as 12T13)	$2$	$4$	$[3/2]$	$[3/2]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{6} + 6 x^{4} + 3$	$[4, 0]$	$[2, 2]$
3.12.15.13	$12$	$x^{12} + 6 x^{4} + 3 x^{3} + 6$	$3$	$12$	$1$	$15$	$C_3\wr D_4$ (as 12T167)	$6$	$4$	$[3/2]$	$[5/4, 5/4, 3/2]_{4}^{6}$	$t + 1$	$x^{12} + 6 x^{4} + 3 x^{3} + 6$	$[4, 0]$	$[1, 2]$
3.12.15.14	$12$	$x^{12} + 3 x^{5} + 3 x^{4} + 3$	$3$	$12$	$1$	$15$	$S_3^2:S_3$ (as 12T116)	$2$	$4$	$[3/2]$	$[5/4, 5/4, 3/2]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{5} + 3 x^{4} + 3$	$[4, 0]$	$[1, 2]$
3.12.15.15	$12$	$x^{12} + 6 x^{4} + 6$	$3$	$12$	$1$	$15$	$(C_6\times C_2):C_2$ (as 12T15)	$2$	$4$	$[3/2]$	$[3/2]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{4} + 6$	$[4, 0]$	$[1, 2]$
3.12.15.16	$12$	$x^{12} + 3 x^{6} + 3 x^{5} + 3 x^{4} + 3$	$3$	$12$	$1$	$15$	$C_3\wr D_4$ (as 12T167)	$6$	$4$	$[3/2]$	$[5/4, 5/4, 3/2]_{4}^{6}$	$t + 1$	$x^{12} + 3 x^{6} + 3 x^{5} + 3 x^{4} + 3$	$[4, 0]$	$[1, 2]$
3.12.15.2	$12$	$x^{12} + 3 x^{6} + 3 x^{4} + 3$	$3$	$12$	$1$	$15$	$C_6\wr C_2$ (as 12T42)	$6$	$4$	$[3/2]$	$[3/2]_{4}^{6}$	$t + 1$	$x^{12} + 3 x^{6} + 3 x^{4} + 3$	$[4, 0]$	$[1, 2]$
3.12.15.3	$12$	$x^{12} + 6 x^{6} + 6 x^{4} + 6$	$3$	$12$	$1$	$15$	$C_6\wr C_2$ (as 12T42)	$6$	$4$	$[3/2]$	$[3/2]_{4}^{6}$	$t + 1$	$x^{12} + 6 x^{6} + 6 x^{4} + 6$	$[4, 0]$	$[1, 2]$
3.12.15.4	$12$	$x^{12} + 6 x^{5} + 6 x^{4} + 6$	$3$	$12$	$1$	$15$	$S_3^2:S_3$ (as 12T116)	$2$	$4$	$[3/2]$	$[5/4, 5/4, 3/2]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{5} + 6 x^{4} + 6$	$[4, 0]$	$[1, 2]$
3.12.15.5	$12$	$x^{12} + 6 x^{6} + 3 x^{4} + 3$	$3$	$12$	$1$	$15$	$C_6\wr C_2$ (as 12T42)	$6$	$4$	$[3/2]$	$[3/2]_{4}^{6}$	$t + 1$	$x^{12} + 6 x^{6} + 3 x^{4} + 3$	$[4, 0]$	$[1, 2]$
3.12.15.6	$12$	$x^{12} + 6 x^{6} + 3 x^{5} + 3 x^{4} + 3$	$3$	$12$	$1$	$15$	$C_3\wr D_4$ (as 12T167)	$6$	$4$	$[3/2]$	$[5/4, 5/4, 3/2]_{4}^{6}$	$t + 1$	$x^{12} + 6 x^{6} + 3 x^{5} + 3 x^{4} + 3$	$[4, 0]$	$[1, 2]$
3.12.15.7	$12$	$x^{12} + 6 x^{6} + 3 x^{4} + 6$	$3$	$12$	$1$	$15$	$(C_6\times C_2):C_2$ (as 12T13)	$2$	$4$	$[3/2]$	$[3/2]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{6} + 3 x^{4} + 6$	$[4, 0]$	$[2, 2]$
3.12.15.8	$12$	$x^{12} + 3 x^{5} + 6 x^{4} + 3$	$3$	$12$	$1$	$15$	$S_3^2:S_3$ (as 12T120)	$2$	$4$	$[3/2]$	$[5/4, 5/4, 3/2]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{5} + 6 x^{4} + 3$	$[4, 0]$	$[2, 2]$
3.12.15.9	$12$	$x^{12} + 3 x^{6} + 3 x^{5} + 6 x^{4} + 6$	$3$	$12$	$1$	$15$	$C_3\wr D_4$ (as 12T167)	$6$	$4$	$[3/2]$	$[5/4, 5/4, 3/2]_{4}^{6}$	$t + 1$	$x^{12} + 3 x^{6} + 3 x^{5} + 6 x^{4} + 6$	$[4, 0]$	$[1, 2]$
3.12.16.47	$12$	$x^{12} + 3 x^{5} + 3$	$3$	$12$	$1$	$16$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[13/8]$	$[13/8, 13/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{5} + 3$	$[5, 0]$	$[1, 2]$
3.12.16.48	$12$	$x^{12} + 6 x^{7} + 3 x^{6} + 3 x^{5} + 6$	$3$	$12$	$1$	$16$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[13/8]$	$[13/8, 13/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{7} + 3 x^{6} + 3 x^{5} + 6$	$[5, 0]$	$[1, 2]$
3.12.16.49	$12$	$x^{12} + 3 x^{8} + 3 x^{7} + 3 x^{5} + 3 x^{3} + 6$	$3$	$12$	$1$	$16$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[13/8]$	$[9/8, 9/8, 13/8, 13/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{8} + 3 x^{7} + 3 x^{5} + 3 x^{3} + 6$	$[5, 0]$	$[1, 2]$
3.12.16.50	$12$	$x^{12} + 3 x^{6} + 3 x^{5} + 6$	$3$	$12$	$1$	$16$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[13/8]$	$[9/8, 9/8, 13/8, 13/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{6} + 3 x^{5} + 6$	$[5, 0]$	$[1, 2]$
3.12.16.51	$12$	$x^{12} + 3 x^{8} + 6 x^{6} + 3 x^{5} + 3$	$3$	$12$	$1$	$16$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[13/8]$	$[9/8, 9/8, 13/8, 13/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{8} + 6 x^{6} + 3 x^{5} + 3$	$[5, 0]$	$[1, 2]$
3.12.16.52	$12$	$x^{12} + 3 x^{8} + 3 x^{6} + 3 x^{5} + 3$	$3$	$12$	$1$	$16$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[13/8]$	$[9/8, 9/8, 13/8, 13/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{8} + 3 x^{6} + 3 x^{5} + 3$	$[5, 0]$	$[1, 2]$
3.12.18.100	$12$	$x^{12} + 6 x^{10} + 6 x^{9} + 3 x^{7} + 6$	$3$	$12$	$1$	$18$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[15/8]$	$[15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{10} + 6 x^{9} + 3 x^{7} + 6$	$[7, 0]$	$[1, 2]$
3.12.18.101	$12$	$x^{12} + 3 x^{11} + 3 x^{7} + 6 x^{6} + 3$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{11} + 3 x^{7} + 6 x^{6} + 3$	$[7, 0]$	$[1, 2]$
3.12.18.102	$12$	$x^{12} + 3 x^{9} + 3 x^{7} + 6 x^{3} + 3$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{9} + 3 x^{7} + 6 x^{3} + 3$	$[7, 0]$	$[1, 2]$
3.12.18.103	$12$	$x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{8} + 6 x^{7} + 3 x^{6} + 6$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{8} + 6 x^{7} + 3 x^{6} + 6$	$[7, 0]$	$[1, 2]$
3.12.18.104	$12$	$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{6} + 3$	$3$	$12$	$1$	$18$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[15/8]$	$[15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{7} + 3 x^{6} + 3$	$[7, 0]$	$[1, 2]$
3.12.18.105	$12$	$x^{12} + 6 x^{11} + 3 x^{7} + 6 x^{6} + 6$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{11} + 3 x^{7} + 6 x^{6} + 6$	$[7, 0]$	$[1, 2]$
3.12.18.106	$12$	$x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{6} + 3$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{11} + 3 x^{10} + 6 x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{6} + 3$	$[7, 0]$	$[1, 2]$
3.12.18.89	$12$	$x^{12} + 3 x^{7} + 3$	$3$	$12$	$1$	$18$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[15/8]$	$[15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{7} + 3$	$[7, 0]$	$[1, 2]$
3.12.18.90	$12$	$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{7} + 3 x^{6} + 6 x^{3} + 3$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{11} + 6 x^{10} + 6 x^{7} + 3 x^{6} + 6 x^{3} + 3$	$[7, 0]$	$[1, 2]$
3.12.18.91	$12$	$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{6} + 6$	$3$	$12$	$1$	$18$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[15/8]$	$[15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{11} + 3 x^{10} + 3 x^{9} + 6 x^{8} + 6 x^{7} + 3 x^{6} + 6$	$[7, 0]$	$[1, 2]$
3.12.18.92	$12$	$x^{12} + 6 x^{11} + 6 x^{9} + 6 x^{8} + 3 x^{7} + 3 x^{6} + 6$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{11} + 6 x^{9} + 6 x^{8} + 3 x^{7} + 3 x^{6} + 6$	$[7, 0]$	$[1, 2]$
3.12.18.93	$12$	$x^{12} + 6 x^{11} + 6 x^{8} + 3 x^{7} + 3$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{11} + 6 x^{8} + 3 x^{7} + 3$	$[7, 0]$	$[1, 2]$
3.12.18.94	$12$	$x^{12} + 3 x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{6} + 3 x^{3} + 3$	$3$	$12$	$1$	$18$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[15/8]$	$[15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{9} + 3 x^{8} + 3 x^{7} + 6 x^{6} + 3 x^{3} + 3$	$[7, 0]$	$[1, 2]$
3.12.18.95	$12$	$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{7} + 6$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{11} + 3 x^{10} + 6 x^{7} + 6$	$[7, 0]$	$[1, 2]$
3.12.18.96	$12$	$x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{7} + 6 x^{6} + 6 x^{3} + 6$	$3$	$12$	$1$	$18$	$F_9:C_2$ (as 12T84)	$2$	$8$	$[15/8]$	$[15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{11} + 3 x^{9} + 3 x^{7} + 6 x^{6} + 6 x^{3} + 6$	$[7, 0]$	$[1, 2]$
3.12.18.97	$12$	$x^{12} + 3 x^{11} + 6 x^{8} + 6 x^{7} + 6 x^{3} + 6$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 3 x^{11} + 6 x^{8} + 6 x^{7} + 6 x^{3} + 6$	$[7, 0]$	$[1, 2]$
3.12.18.98	$12$	$x^{12} + 6 x^{11} + 3 x^{9} + 6 x^{7} + 3 x^{6} + 6 x^{3} + 6$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{11} + 3 x^{9} + 6 x^{7} + 3 x^{6} + 6 x^{3} + 6$	$[7, 0]$	$[1, 2]$
3.12.18.99	$12$	$x^{12} + 6 x^{11} + 3 x^{7} + 3 x^{6} + 3$	$3$	$12$	$1$	$18$	$C_3^4:\SD_{16}$ (as 12T212)	$2$	$8$	$[15/8]$	$[9/8, 9/8, 15/8, 15/8]_{8}^{2}$	$t + 1$	$x^{12} + 6 x^{11} + 3 x^{7} + 3 x^{6} + 3$	$[7, 0]$	$[1, 2]$
3.12.19.1	$12$	$x^{12} + 3 x^{8} + 3$	$3$	$12$	$1$	$19$	$D_{12}$ (as 12T12)	$2$	$4$	$[2]$	$[2]_{4}^{2}$	$t + 1$	$x^{12} + 3 x^{8} + 3$	$[8, 0]$	$[2, 2]$
3.12.19.10	$12$	$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 24$	$3$	$12$	$1$	$19$	$C_6\wr C_2$ (as 12T42)	$2$	$4$	$[2]$	$[3/2, 2]_{4}^{2}$	$t + 1$	$x^{12} + 6 x^{11} + 3 x^{10} + 3 x^{9} + 3 x^{8} + 3 x^{6} + 24$	$[8, 0]$	$[1, 2]$

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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.