$p$-adic field search results

Degree	Discriminant exponent	Galois group
Residue characteristic	Ramification index	Top slope

Results (8 matches)

 

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