$p$-adic field search results

Degree	Discriminant exponent	Galois group
Residue characteristic	Ramification index	Top slope

Results (11 matches)

 

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
5.8.0.1	x^8 + x^2 - 2x + 3	$5$	$1$	$8$	$0$	$C_8$ (as 8T1)	$ [\ ]^{8}$
5.8.4.1	x^8 + 10x^6 + 125x^4 + 2500	$5$	$2$	$4$	$4$	$C_4\times C_2$ (as 8T2)	$ [\ ]_{2}^{4}$
5.8.4.2	x^8 + 25x^4 - 250x^2 + 1250	$5$	$2$	$4$	$4$	$C_8$ (as 8T1)	$ [\ ]_{2}^{4}$
5.8.6.1	x^8 - 5x^4 + 400	$5$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$ [\ ]_{4}^{2}$
5.8.6.2	x^8 + 15x^4 + 100	$5$	$4$	$2$	$6$	$C_4\times C_2$ (as 8T2)	$ [\ ]_{4}^{2}$
5.8.6.3	x^8 + 25x^4 + 200	$5$	$4$	$2$	$6$	$C_8$ (as 8T1)	$ [\ ]_{4}^{2}$
5.8.6.4	x^8 - 5x^4 + 50	$5$	$4$	$2$	$6$	$C_8$ (as 8T1)	$ [\ ]_{4}^{2}$
5.8.7.1	x^8 - 5	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$ [\ ]_{8}^{2}$
5.8.7.2	x^8 - 20	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$ [\ ]_{8}^{2}$
5.8.7.3	x^8 + 10	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$ [\ ]_{8}^{2}$
5.8.7.4	x^8 + 40	$5$	$8$	$1$	$7$	$C_8:C_2$ (as 8T7)	$ [\ ]_{8}^{2}$