$p$-adic field search results

Degree	Discriminant exponent	Galois group
Residue characteristic	Ramification index	Top slope

Results (6 matches)

 

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
17.10.0.1	x^10 - x + 7	$17$	$1$	$10$	$0$	$C_{10}$ (as 10T1)	$ [\ ]^{10}$
17.10.5.1	x^10 - 578x^6 + 83521x^2 - 51114852	$17$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$ [\ ]_{2}^{5}$
17.10.5.2	x^10 - 83521x^2 + 8519142	$17$	$2$	$5$	$5$	$C_{10}$ (as 10T1)	$ [\ ]_{2}^{5}$
17.10.8.1	x^10 - 17x^5 + 867	$17$	$5$	$2$	$8$	$F_5$ (as 10T4)	$ [\ ]_{5}^{4}$
17.10.9.1	x^10 - 17	$17$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$ [\ ]_{10}^{4}$
17.10.9.2	x^10 + 51	$17$	$10$	$1$	$9$	$F_{5}\times C_2$ (as 10T5)	$ [\ ]_{10}^{4}$