Local Number Field Search Results

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

Results (displaying all 20 matches)

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
19.12.0.1	x^12 - x + 15	19	1	12	0	$C_{12}$ (as 12T1)	$ [\ ]^{12}$
19.12.6.1	x^12 + 41154x^6 - 2476099x^2 + 423412929	19	2	6	6	$C_6\times C_2$ (as 12T2)	$ [\ ]_{2}^{6}$
19.12.6.2	x^12 - 2476099x^2 + 141137643	19	2	6	6	$C_{12}$ (as 12T1)	$ [\ ]_{2}^{6}$
19.12.8.1	x^12 - 114x^9 + 4332x^6 - 54872x^3 + 130321000	19	3	4	8	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
19.12.8.2	x^12 - 13718x^3 + 1303210	19	3	4	8	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
19.12.8.3	x^12 + 7220x^6 - 27436x^3 + 13032100	19	3	4	8	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
19.12.9.1	x^12 - 361x^4 + 27436	19	4	3	9	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{4}^{6}$
19.12.9.2	x^12 - 38x^8 + 361x^4 - 109744	19	4	3	9	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{4}^{6}$
19.12.10.1	x^12 - 171x^6 + 23104	19	6	2	10	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
19.12.10.2	x^12 + 57x^6 + 1444	19	6	2	10	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
19.12.10.3	x^12 - 19x^6 + 5776	19	6	2	10	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
19.12.10.4	x^12 - 19x^6 + 722	19	6	2	10	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
19.12.10.5	x^12 + 95x^6 + 2888	19	6	2	10	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
19.12.10.6	x^12 - 209x^6 + 11552	19	6	2	10	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
19.12.11.1	x^12 + 76	19	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
19.12.11.2	x^12 + 1216	19	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
19.12.11.3	x^12 + 19456	19	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
19.12.11.4	x^12 - 19	19	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
19.12.11.5	x^12 - 304	19	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$
19.12.11.6	x^12 - 4864	19	12	1	11	$D_4 \times C_3$ (as 12T14)	$ [\ ]_{12}^{2}$