$p$-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
19.15.0.1	$15$	x^15 + x^2 + 4	$19$	$1$	$15$	$0$	$C_{15}$ (as 15T1)	$15$	$1$	$[\ ]^{15}$
19.15.10.1	$15$	x^15 + 102885x^6 - 130321x^3 + 309512375	$19$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]_{3}^{5}$
19.15.10.2	$15$	x^15 - 130321x^3 + 12380495	$19$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]_{3}^{5}$
19.15.10.3	$15$	x^15 - 722x^9 + 130321x^3 - 61902475	$19$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$5$	$3$	$[\ ]_{3}^{5}$
19.15.12.1	$15$	x^15 - 361x^5 + 27436	$19$	$5$	$3$	$12$	$D_5\times C_3$ (as 15T3)	$6$	$5$	$[\ ]_{5}^{6}$
19.15.14.1	$15$	x^15 - 19	$19$	$15$	$1$	$14$	$D_5\times C_3$ (as 15T3)	$2$	$15$	$[\ ]_{15}^{2}$
19.15.14.2	$15$	x^15 + 76	$19$	$15$	$1$	$14$	$D_5\times C_3$ (as 15T3)	$2$	$15$	$[\ ]_{15}^{2}$
19.15.14.3	$15$	x^15 - 304	$19$	$15$	$1$	$14$	$D_5\times C_3$ (as 15T3)	$2$	$15$	$[\ ]_{15}^{2}$