Local number field search results

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

Results (displaying all 11 matches)

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
13.8.0.1	x^8 + 4x^2 - x + 6	13	1	8	0	$C_8$ (as 8T1)	$ [\ ]^{8}$
13.8.4.1	x^8 + 26x^6 + 845x^4 + 6591x^2 + 114244	13	2	4	4	$C_4\times C_2$ (as 8T2)	$ [\ ]_{2}^{4}$
13.8.4.2	x^8 + 169x^4 - 2197x^2 + 57122	13	2	4	4	$C_8$ (as 8T1)	$ [\ ]_{2}^{4}$
13.8.6.1	x^8 - 13x^4 + 2704	13	4	2	6	$C_4\times C_2$ (as 8T2)	$ [\ ]_{4}^{2}$
13.8.6.2	x^8 + 39x^4 + 676	13	4	2	6	$C_4\times C_2$ (as 8T2)	$ [\ ]_{4}^{2}$
13.8.6.3	x^8 + 65x^4 + 1352	13	4	2	6	$C_8$ (as 8T1)	$ [\ ]_{4}^{2}$
13.8.6.4	x^8 - 13x^4 + 338	13	4	2	6	$C_8$ (as 8T1)	$ [\ ]_{4}^{2}$
13.8.7.1	x^8 - 13	13	8	1	7	$C_8:C_2$ (as 8T7)	$ [\ ]_{8}^{2}$
13.8.7.2	x^8 - 52	13	8	1	7	$C_8:C_2$ (as 8T7)	$ [\ ]_{8}^{2}$
13.8.7.3	x^8 + 26	13	8	1	7	$C_8:C_2$ (as 8T7)	$ [\ ]_{8}^{2}$
13.8.7.4	x^8 + 104	13	8	1	7	$C_8:C_2$ (as 8T7)	$ [\ ]_{8}^{2}$