Local number field search results

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

Results (displaying all 13 matches)

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
11.12.0.1	x^12 - x + 7	11	1	12	0	$C_{12}$ (as 12T1)	$ [\ ]^{12}$
11.12.6.1	x^12 + 242x^8 + 21296x^6 + 14641x^4 + 1932612x^2 + 113379904	11	2	6	6	$C_6\times C_2$ (as 12T2)	$ [\ ]_{2}^{6}$
11.12.6.2	x^12 + 14641x^4 - 322102x^2 + 14172488	11	2	6	6	$C_{12}$ (as 12T1)	$ [\ ]_{2}^{6}$
11.12.8.1	x^12 - 33x^9 + 363x^6 - 1331x^3 + 117128	11	3	4	8	$C_3 : C_4$ (as 12T5)	$ [\ ]_{3}^{4}$
11.12.8.2	x^12 - 1331x^3 + 29282	11	3	4	8	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [\ ]_{3}^{12}$
11.12.9.1	x^12 - 121x^4 + 3993	11	4	3	9	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{4}^{6}$
11.12.9.2	x^12 - 22x^8 + 121x^4 - 11979	11	4	3	9	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{4}^{6}$
11.12.10.1	x^12 + 3146x^6 + 14235529	11	6	2	10	$D_6$ (as 12T3)	$ [\ ]_{6}^{2}$
11.12.10.2	x^12 + 143x^6 + 5929	11	6	2	10	$C_6\times S_3$ (as 12T18)	$ [\ ]_{6}^{6}$
11.12.10.3	x^12 + 220x^6 + 41503	11	6	2	10	$C_3 : C_4$ (as 12T5)	$ [\ ]_{6}^{2}$
11.12.10.4	x^12 - 11x^6 + 847	11	6	2	10	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [\ ]_{6}^{6}$
11.12.11.1	x^12 + 33	11	12	1	11	$D_{12}$ (as 12T12)	$ [\ ]_{12}^{2}$
11.12.11.2	x^12 - 11	11	12	1	11	$D_{12}$ (as 12T12)	$ [\ ]_{12}^{2}$