$p$-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 (8 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Slope content
19.10.0.1	$10$	x^10 + x^2 - 2x + 14	$19$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$10$	$1$	$[\ ]^{10}$
19.10.5.1	$10$	x^10 - 722x^6 + 130321x^2 - 61902475	$19$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]_{2}^{5}$
19.10.5.2	$10$	x^10 - 130321x^2 + 12380495	$19$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$5$	$2$	$[\ ]_{2}^{5}$
19.10.8.1	$10$	x^10 - 209x^5 + 11552	$19$	$5$	$2$	$8$	$D_5$ (as 10T2)	$2$	$5$	$[\ ]_{5}^{2}$
19.10.8.2	$10$	x^10 - 19x^5 + 722	$19$	$5$	$2$	$8$	$D_5\times C_5$ (as 10T6)	$10$	$5$	$[\ ]_{5}^{10}$
19.10.8.3	$10$	x^10 + 57x^5 + 1444	$19$	$5$	$2$	$8$	$D_5\times C_5$ (as 10T6)	$10$	$5$	$[\ ]_{5}^{10}$
19.10.9.1	$10$	x^10 - 19	$19$	$10$	$1$	$9$	$D_{10}$ (as 10T3)	$2$	$10$	$[\ ]_{10}^{2}$
19.10.9.2	$10$	x^10 + 76	$19$	$10$	$1$	$9$	$D_{10}$ (as 10T3)	$2$	$10$	$[\ ]_{10}^{2}$