$p$-adic field search results

Degree	Discriminant exponent	Galois group
Residue characteristic	Ramification index	Top slope

Results (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}$