Local number field search results

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

Results (displaying all 8 matches)

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
23.8.0.1	x^8 + x^2 - 2x + 5	23	1	8	0	$C_8$ (as 8T1)	$ [\ ]^{8}$
23.8.4.1	x^8 + 11638x^4 - 12167x^2 + 33860761	23	2	4	4	$C_4\times C_2$ (as 8T2)	$ [\ ]_{2}^{4}$
23.8.4.2	x^8 - 12167x^2 + 3078251	23	2	4	4	$C_8$ (as 8T1)	$ [\ ]_{2}^{4}$
23.8.6.1	x^8 + 299x^4 + 25921	23	4	2	6	$Q_8$ (as 8T5)	$ [\ ]_{4}^{2}$
23.8.6.2	x^8 - 1633x^4 + 1270129	23	4	2	6	$D_4$ (as 8T4)	$ [\ ]_{4}^{2}$
23.8.6.3	x^8 - 23x^4 + 3703	23	4	2	6	$C_8:C_2$ (as 8T7)	$ [\ ]_{4}^{4}$
23.8.7.1	x^8 + 46	23	8	1	7	$D_{8}$ (as 8T6)	$ [\ ]_{8}^{2}$
23.8.7.2	x^8 - 23	23	8	1	7	$D_{8}$ (as 8T6)	$ [\ ]_{8}^{2}$