Local Number Field Search Results

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

Results (displaying all 20 matches)

Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
x^12 + 3x^2 - 2x + 3	7	1	12	0	$C_{12}$ (as 12T1)	$ [\ ]^{12}$
x^12 + 294x^8 + 3430x^6 + 21609x^4 + 487403x^2 + 2941225	7	2	6	6	$C_6\times C_2$ (as 12T2)	$ [\ ]_{2}^{6}$
x^12 + 7203x^4 - 16807x^2 + 588245	7	2	6	6	$C_{12}$ (as 12T1)	$ [\ ]_{2}^{6}$
x^12 - 63x^9 + 637x^6 + 6174x^3 + 300125	7	3	4	8	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
x^12 + 49x^6 - 1029x^3 + 12005	7	3	4	8	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
x^12 + 14x^9 + 539x^6 + 343x^3 + 60025	7	3	4	8	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
x^12 - 49x^4 + 686	7	4	3	9	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{4}^{6}$
x^12 - 14x^8 + 49x^4 - 1372	7	4	3	9	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{4}^{6}$
x^12 - 70x^6 + 35721	7	6	2	10	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
x^12 + 35x^6 + 441	7	6	2	10	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
x^12 - 49x^6 + 3969	7	6	2	10	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
x^12 - 7x^6 + 147	7	6	2	10	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
x^12 + 56x^6 + 1323	7	6	2	10	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
x^12 - 217x^6 + 11907	7	6	2	10	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
x^12 + 14	7	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
x^12 + 56	7	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
x^12 + 224	7	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
x^12 - 7	7	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
x^12 - 28	7	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
x^12 - 112	7	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$

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