$p$-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 (6 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
11.14.0.1	$14$	x^14 + x^2 - 5x + 8	$11$	$1$	$14$	$0$	$C_{14}$ (as 14T1)	$14$	$1$	$[\ ]^{14}$
11.14.7.1	$14$	x^14 - 2662x^8 + 1771561x^2 - 311794736	$11$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$7$	$2$	$[\ ]_{2}^{7}$
11.14.7.2	$14$	x^14 - 1771561x^2 + 77948684	$11$	$2$	$7$	$7$	$C_{14}$ (as 14T1)	$7$	$2$	$[\ ]_{2}^{7}$
11.14.12.1	$14$	x^14 - 11x^7 + 847	$11$	$7$	$2$	$12$	$(C_7:C_3) \times C_2$ (as 14T5)	$6$	$7$	$[\ ]_{7}^{6}$
11.14.13.1	$14$	x^14 - 11	$11$	$14$	$1$	$13$	$(C_7:C_3) \times C_2$ (as 14T5)	$3$	$14$	$[\ ]_{14}^{3}$
11.14.13.2	$14$	x^14 + 33	$11$	$14$	$1$	$13$	$(C_7:C_3) \times C_2$ (as 14T5)	$3$	$14$	$[\ ]_{14}^{3}$