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
23.12.0.1	x^12 + x^2 - 3x + 7	23	1	12	0	$C_{12}$ (as 12T1)	$ [\ ]^{12}$
23.12.6.1	x^12 + 365010x^6 - 6436343x^2 + 33308075025	23	2	6	6	$C_6\times C_2$ (as 12T2)	$ [\ ]_{2}^{6}$
23.12.6.2	x^12 - 6436343x^2 + 2220538335	23	2	6	6	$C_{12}$ (as 12T1)	$ [\ ]_{2}^{6}$
23.12.8.1	x^12 - 69x^9 + 1587x^6 - 12167x^3 + 372468371	23	3	4	8	$C_3 : C_4$ (as 12T5)	$ [\ ]_{3}^{4}$
23.12.8.2	x^12 - 12167x^3 + 3078251	23	3	4	8	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [\ ]_{3}^{12}$
23.12.9.1	x^12 - 529x^4 + 48668	23	4	3	9	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{4}^{6}$
23.12.9.2	x^12 - 46x^8 + 529x^4 - 194672	23	4	3	9	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{4}^{6}$
23.12.10.1	x^12 + 6578x^6 + 62236321	23	6	2	10	$D_6$ (as 12T3)	$ [\ ]_{6}^{2}$
23.12.10.2	x^12 + 299x^6 + 25921	23	6	2	10	$C_6\times S_3$ (as 12T18)	$ [\ ]_{6}^{6}$
23.12.10.3	x^12 + 460x^6 + 181447	23	6	2	10	$C_3 : C_4$ (as 12T5)	$ [\ ]_{6}^{2}$
23.12.10.4	x^12 - 23x^6 + 3703	23	6	2	10	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [\ ]_{6}^{6}$
23.12.11.1	x^12 + 46	23	12	1	11	$D_{12}$ (as 12T12)	$ [\ ]_{12}^{2}$
23.12.11.2	x^12 - 23	23	12	1	11	$D_{12}$ (as 12T12)	$ [\ ]_{12}^{2}$