$p$-adic field search results

Degree	Discriminant exponent	Galois group
Residue characteristic	Ramification index	Top slope

Results (10 matches)

 

Label	Polynomial	$p$	$e$	$f$	$c$	Galois group	Slope content
3.3.0.1	x^3 - x + 1	$3$	$1$	$3$	$0$	$C_3$ (as 3T1)	$ [\ ]^{3}$
3.3.3.1	x^3 + 6x + 3	$3$	$3$	$1$	$3$	$S_3$ (as 3T2)	$ [3/2]_{2}$
3.3.3.2	x^3 + 3x + 3	$3$	$3$	$1$	$3$	$S_3$ (as 3T2)	$ [3/2]_{2}$
3.3.4.1	x^3 - 3x^2 + 21	$3$	$3$	$1$	$4$	$C_3$ (as 3T1)	$ [2]$
3.3.4.2	x^3 - 3x^2 + 3	$3$	$3$	$1$	$4$	$C_3$ (as 3T1)	$ [2]$
3.3.4.3	x^3 - 3x^2 + 12	$3$	$3$	$1$	$4$	$C_3$ (as 3T1)	$ [2]$
3.3.4.4	x^3 + 3x^2 + 3	$3$	$3$	$1$	$4$	$S_3$ (as 3T2)	$ [2]^{2}$
3.3.5.1	x^3 + 3	$3$	$3$	$1$	$5$	$S_3$ (as 3T2)	$ [5/2]_{2}$
3.3.5.2	x^3 + 21	$3$	$3$	$1$	$5$	$S_3$ (as 3T2)	$ [5/2]_{2}$
3.3.5.3	x^3 + 12	$3$	$3$	$1$	$5$	$S_3$ (as 3T2)	$ [5/2]_{2}$