$p$-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 (7 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
5.6.0.1	$6$	x^6 - x + 2	$5$	$1$	$6$	$0$	$C_6$ (as 6T1)	$6$	$1$	$[\ ]^{6}$
5.6.3.1	$6$	x^6 - 10x^4 + 25x^2 - 500	$5$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]_{2}^{3}$
5.6.3.2	$6$	x^6 - 25x^2 + 250	$5$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]_{2}^{3}$
5.6.4.1	$6$	x^6 + 25x^3 + 200	$5$	$3$	$2$	$4$	$S_3$ (as 6T2)	$2$	$3$	$[\ ]_{3}^{2}$
5.6.4.2	$6$	x^6 - 5x^3 + 50	$5$	$3$	$2$	$4$	$S_3\times C_3$ (as 6T5)	$6$	$3$	$[\ ]_{3}^{6}$
5.6.5.1	$6$	x^6 - 5	$5$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$2$	$6$	$[\ ]_{6}^{2}$
5.6.5.2	$6$	x^6 + 10	$5$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$2$	$6$	$[\ ]_{6}^{2}$