$p$-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
7.15.0.1	x^15 + 3x^2 - 2x + 2	$7$	$1$	$15$	$0$	$C_{15}$ (as 15T1)	$ [\ ]^{15}$
7.15.10.1	x^15 + 4116x^6 - 2401x^3 + 1075648	$7$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$ [\ ]_{3}^{5}$
7.15.10.2	x^15 - 2401x^3 + 67228	$7$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$ [\ ]_{3}^{5}$
7.15.10.3	x^15 - 98x^9 + 2401x^3 - 268912	$7$	$3$	$5$	$10$	$C_{15}$ (as 15T1)	$ [\ ]_{3}^{5}$
7.15.12.1	x^15 - 49x^5 + 686	$7$	$5$	$3$	$12$	$F_5\times C_3$ (as 15T8)	$ [\ ]_{5}^{12}$
7.15.14.1	x^15 - 7	$7$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$ [\ ]_{15}^{4}$
7.15.14.2	x^15 + 14	$7$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$ [\ ]_{15}^{4}$
7.15.14.3	x^15 - 28	$7$	$15$	$1$	$14$	$F_5\times C_3$ (as 15T8)	$ [\ ]_{15}^{4}$