$p$-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
19.6.0.1	$6$	x^6 - x + 3	$19$	$1$	$6$	$0$	$C_6$ (as 6T1)	$6$	$1$	$[\ ]^{6}$
19.6.3.1	$6$	x^6 - 38x^4 + 361x^2 - 109744	$19$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]_{2}^{3}$
19.6.3.2	$6$	x^6 - 361x^2 + 27436	$19$	$2$	$3$	$3$	$C_6$ (as 6T1)	$3$	$2$	$[\ ]_{2}^{3}$
19.6.4.1	$6$	x^6 + 57x^3 + 1444	$19$	$3$	$2$	$4$	$C_6$ (as 6T1)	$2$	$3$	$[\ ]_{3}^{2}$
19.6.4.2	$6$	x^6 - 19x^3 + 722	$19$	$3$	$2$	$4$	$C_6$ (as 6T1)	$2$	$3$	$[\ ]_{3}^{2}$
19.6.4.3	$6$	x^6 + 95x^3 + 2888	$19$	$3$	$2$	$4$	$C_6$ (as 6T1)	$2$	$3$	$[\ ]_{3}^{2}$
19.6.5.1	$6$	x^6 - 304	$19$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
19.6.5.2	$6$	x^6 - 19	$19$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
19.6.5.3	$6$	x^6 - 4864	$19$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
19.6.5.4	$6$	x^6 + 76	$19$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
19.6.5.5	$6$	x^6 + 1216	$19$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$
19.6.5.6	$6$	x^6 + 19456	$19$	$6$	$1$	$5$	$C_6$ (as 6T1)	$1$	$6$	$[\ ]_{6}$