$p$-adic field search results

Degree	Residue characteristic	Galois group	Galois unramified degree
Ramification index	Discriminant exponent	Inertia subgroup	Galois tame degree
Residue field degree	Top slope	Wild inertia subgroup

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Results (13 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
11.12.0.1	$12$	x^12 - x + 7	$11$	$1$	$12$	$0$	$C_{12}$ (as 12T1)	$12$	$1$	$[\ ]^{12}$
11.12.6.1	$12$	x^12 + 242x^8 + 21296x^6 + 14641x^4 + 1932612x^2 + 113379904	$11$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$6$	$2$	$[\ ]_{2}^{6}$
11.12.6.2	$12$	x^12 + 14641x^4 - 322102x^2 + 14172488	$11$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$6$	$2$	$[\ ]_{2}^{6}$
11.12.8.1	$12$	x^12 - 33x^9 + 363x^6 - 1331x^3 + 117128	$11$	$3$	$4$	$8$	$C_3 : C_4$ (as 12T5)	$4$	$3$	$[\ ]_{3}^{4}$
11.12.8.2	$12$	x^12 - 1331x^3 + 29282	$11$	$3$	$4$	$8$	$C_3\times (C_3 : C_4)$ (as 12T19)	$12$	$3$	$[\ ]_{3}^{12}$
11.12.9.1	$12$	x^12 - 121x^4 + 3993	$11$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]_{4}^{6}$
11.12.9.2	$12$	x^12 - 22x^8 + 121x^4 - 11979	$11$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]_{4}^{6}$
11.12.10.1	$12$	x^12 + 3146x^6 + 14235529	$11$	$6$	$2$	$10$	$D_6$ (as 12T3)	$2$	$6$	$[\ ]_{6}^{2}$
11.12.10.2	$12$	x^12 + 143x^6 + 5929	$11$	$6$	$2$	$10$	$C_6\times S_3$ (as 12T18)	$6$	$6$	$[\ ]_{6}^{6}$
11.12.10.3	$12$	x^12 + 220x^6 + 41503	$11$	$6$	$2$	$10$	$C_3 : C_4$ (as 12T5)	$2$	$6$	$[\ ]_{6}^{2}$
11.12.10.4	$12$	x^12 - 11x^6 + 847	$11$	$6$	$2$	$10$	$C_3\times (C_3 : C_4)$ (as 12T19)	$6$	$6$	$[\ ]_{6}^{6}$
11.12.11.1	$12$	x^12 + 33	$11$	$12$	$1$	$11$	$D_{12}$ (as 12T12)	$2$	$12$	$[\ ]_{12}^{2}$
11.12.11.2	$12$	x^12 - 11	$11$	$12$	$1$	$11$	$D_{12}$ (as 12T12)	$2$	$12$	$[\ ]_{12}^{2}$