$p$-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 (12 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
7.6.0.1	$6$	x^6 + 3x^2 - x + 5	$7$	$1$	$6$	$0$	$C_6$ (as 6T1)	$6$	$1$	$[\ ]^{6}$
7.6.3.1	$6$	x^6 - 14x^4 + 49x^2 - 1372	$7$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]_{2}^{3}$
7.6.3.2	$6$	x^6 - 49x^2 + 686	$7$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]_{2}^{3}$
7.6.4.1	$6$	x^6 + 35x^3 + 441	$7$	$3$	$2$	$4$	$C_6$ (as 6T1)	$2$	$3$	$[\ ]_{3}^{2}$
7.6.4.2	$6$	x^6 - 7x^3 + 147	$7$	$3$	$2$	$4$	$C_6$ (as 6T1)	$2$	$3$	$[\ ]_{3}^{2}$
7.6.4.3	$6$	x^6 + 56x^3 + 1323	$7$	$3$	$2$	$4$	$C_6$ (as 6T1)	$2$	$3$	$[\ ]_{3}^{2}$
7.6.5.1	$6$	x^6 - 28	$7$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
7.6.5.2	$6$	x^6 - 7	$7$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
7.6.5.3	$6$	x^6 - 112	$7$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
7.6.5.4	$6$	x^6 + 14	$7$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
7.6.5.5	$6$	x^6 + 56	$7$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
7.6.5.6	$6$	x^6 + 224	$7$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$