$p$-adic field search results

Degree	Discriminant exponent	Galois group
Residue characteristic	Ramification index	Top slope

Results (28 matches)

 

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
13.12.0.1	x^12 + x^2 - x + 2	$13$	$1$	$12$	$0$	$C_{12}$ (as 12T1)	$ [\ ]^{12}$
13.12.6.1	x^12 + 338x^8 + 8788x^6 + 28561x^4 + 19307236	$13$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$ [\ ]_{2}^{6}$
13.12.6.2	x^12 + 28561x^4 - 742586x^2 + 9653618	$13$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$ [\ ]_{2}^{6}$
13.12.8.1	x^12 - 39x^9 - 338x^6 + 10985x^3 + 228488	$13$	$3$	$4$	$8$	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
13.12.8.2	x^12 + 169x^6 - 2197x^3 + 57122	$13$	$3$	$4$	$8$	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
13.12.8.3	x^12 + 26x^9 + 845x^6 + 6591x^3 + 114244	$13$	$3$	$4$	$8$	$C_{12}$ (as 12T1)	$ [\ ]_{3}^{4}$
13.12.9.1	x^12 - 104x^8 - 45968x^4 - 2847312	$13$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
13.12.9.2	x^12 - 52x^8 + 676x^4 - 79092	$13$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
13.12.9.3	x^12 - 338x^4 + 13182	$13$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
13.12.9.4	x^12 + 234x^8 + 16900x^4 + 474552	$13$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$ [\ ]_{4}^{3}$
13.12.10.1	x^12 - 117x^6 + 10816	$13$	$6$	$2$	$10$	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
13.12.10.2	x^12 + 39x^6 + 676	$13$	$6$	$2$	$10$	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
13.12.10.3	x^12 - 13x^6 + 2704	$13$	$6$	$2$	$10$	$C_6\times C_2$ (as 12T2)	$ [\ ]_{6}^{2}$
13.12.10.4	x^12 - 13x^6 + 338	$13$	$6$	$2$	$10$	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
13.12.10.5	x^12 + 65x^6 + 1352	$13$	$6$	$2$	$10$	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
13.12.10.6	x^12 - 143x^6 + 5408	$13$	$6$	$2$	$10$	$C_{12}$ (as 12T1)	$ [\ ]_{6}^{2}$
13.12.11.1	x^12 - 13	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.10	x^12 + 1664	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.11	x^12 + 6656	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.12	x^12 + 26624	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.2	x^12 - 52	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.3	x^12 - 208	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.4	x^12 - 832	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.5	x^12 - 3328	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.6	x^12 - 13312	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.7	x^12 + 26	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.8	x^12 + 104	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$
13.12.11.9	x^12 + 416	$13$	$12$	$1$	$11$	$C_{12}$ (as 12T1)	$ [\ ]_{12}$