Local number field search results

Degree	Discriminant exponent $c$	Galois group
Prime $p$	Ramification index $e$	Top slope

Results (displaying all 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}$