$p$-adic field search results

Degree	Discriminant exponent	Galois group
Residue characteristic	Ramification index	Top slope

Results (7 matches)

 

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
17.6.0.1	x^6 - x + 12	$17$	$1$	$6$	$0$	$C_6$ (as 6T1)	$ [\ ]^{6}$
17.6.3.1	x^6 - 34x^4 + 289x^2 - 44217	$17$	$2$	$3$	$3$	$C_6$ (as 6T1)	$ [\ ]_{2}^{3}$
17.6.3.2	x^6 - 289x^2 + 14739	$17$	$2$	$3$	$3$	$C_6$ (as 6T1)	$ [\ ]_{2}^{3}$
17.6.4.1	x^6 + 136x^3 + 7803	$17$	$3$	$2$	$4$	$S_3$ (as 6T2)	$ [\ ]_{3}^{2}$
17.6.4.2	x^6 - 17x^3 + 867	$17$	$3$	$2$	$4$	$S_3\times C_3$ (as 6T5)	$ [\ ]_{3}^{6}$
17.6.5.1	x^6 - 17	$17$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$ [\ ]_{6}^{2}$
17.6.5.2	x^6 + 51	$17$	$6$	$1$	$5$	$D_{6}$ (as 6T3)	$ [\ ]_{6}^{2}$