Local Number Field Search Results

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

Results (displaying all 17 matches)

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
17.12.0.1	x^12 + 3x^2 - 2x + 5	17	1	12	0	$C_{12}$ (as 12T1)	$ [\ ]^{12}$
17.12.6.1	x^12 + 117912x^6 - 1419857x^2 + 3475809936	17	2	6	6	$C_6\times C_2$ (as 12T2)	$ [\ ]_{2}^{6}$
17.12.6.2	x^12 - 1419857x^2 + 289650828	17	2	6	6	$C_{12}$ (as 12T1)	$ [\ ]_{2}^{6}$
17.12.8.1	x^12 - 51x^9 + 867x^6 - 4913x^3 + 111166451	17	3	4	8	$C_3 : C_4$ (as 12T5)	$ [\ ]_{3}^{4}$
17.12.8.2	x^12 - 4913x^3 + 918731	17	3	4	8	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [\ ]_{3}^{12}$
17.12.9.1	x^12 - 34x^8 - 10115x^4 - 397953	17	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
17.12.9.2	x^12 - 34x^8 + 289x^4 - 44217	17	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
17.12.9.3	x^12 - 289x^4 + 14739	17	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
17.12.9.4	x^12 + 153x^8 + 7514x^4 + 132651	17	4	3	9	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
17.12.10.1	x^12 - 170x^6 + 210681	17	6	2	10	$D_6$ (as 12T3)	$ [\ ]_{6}^{2}$
17.12.10.2	x^12 + 85x^6 + 2601	17	6	2	10	$C_6\times S_3$ (as 12T18)	$ [\ ]_{6}^{6}$
17.12.10.3	x^12 + 136x^6 + 7803	17	6	2	10	$C_3 : C_4$ (as 12T5)	$ [\ ]_{6}^{2}$
17.12.10.4	x^12 - 17x^6 + 867	17	6	2	10	$C_3\times (C_3 : C_4)$ (as 12T19)	$ [\ ]_{6}^{6}$
17.12.11.1	x^12 - 17	17	12	1	11	$S_3 \times C_4$ (as 12T11)	$ [\ ]_{12}^{2}$
17.12.11.2	x^12 - 153	17	12	1	11	$S_3 \times C_4$ (as 12T11)	$ [\ ]_{12}^{2}$
17.12.11.3	x^12 + 51	17	12	1	11	$S_3 \times C_4$ (as 12T11)	$ [\ ]_{12}^{2}$
17.12.11.4	x^12 + 459	17	12	1	11	$S_3 \times C_4$ (as 12T11)	$ [\ ]_{12}^{2}$