$p$-adic field search results

Results (8 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
2.14.18.1	$14$	$x^{14} + 2 x^{10} + 2 x^{5} + 2$	$2$	$14$	$1$	$18$	$F_8:C_3$ (as 14T11)	$3$	$7$	$[12/7]$	$[12/7, 12/7, 12/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{10} + 2 x^{5} + 2$	$[5, 0]$	$[1, 3]$
2.14.18.2	$14$	$x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2$	$2$	$14$	$1$	$18$	$F_8:C_3$ (as 14T11)	$3$	$7$	$[12/7]$	$[12/7, 12/7, 12/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2$	$[5, 0]$	$[1, 3]$
2.14.18.3	$14$	$x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{5} + 2$	$2$	$14$	$1$	$18$	$C_2^3:F_8:C_3$ (as 14T35)	$3$	$7$	$[12/7]$	$[8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{5} + 2$	$[5, 0]$	$[1, 3]$
2.14.18.4	$14$	$x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2$	$2$	$14$	$1$	$18$	$C_2\wr C_7:C_3$ (as 14T44)	$6$	$7$	$[12/7]$	$[8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{6} + 2 x^{5} + 2$	$[5, 0]$	$[1, 3]$
2.14.18.5	$14$	$x^{14} + 2 x^{9} + 2 x^{6} + 2 x^{5} + 2$	$2$	$14$	$1$	$18$	$F_8:C_6$ (as 14T18)	$6$	$7$	$[12/7]$	$[12/7, 12/7, 12/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{9} + 2 x^{6} + 2 x^{5} + 2$	$[5, 0]$	$[1, 3]$
2.14.18.6	$14$	$x^{14} + 2 x^{10} + 2 x^{7} + 2 x^{5} + 2$	$2$	$14$	$1$	$18$	$C_2^3:F_8:C_3$ (as 14T35)	$3$	$7$	$[12/7]$	$[8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{3}$	$t + 1$	$x^{14} + 2 x^{10} + 2 x^{7} + 2 x^{5} + 2$	$[5, 0]$	$[1, 3]$
2.14.18.7	$14$	$x^{14} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$	$2$	$14$	$1$	$18$	$F_8:C_6$ (as 14T18)	$6$	$7$	$[12/7]$	$[12/7, 12/7, 12/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{8} + 2 x^{7} + 2 x^{5} + 2$	$[5, 0]$	$[1, 3]$
2.14.18.8	$14$	$x^{14} + 2 x^{6} + 2 x^{5} + 2$	$2$	$14$	$1$	$18$	$C_2\wr C_7:C_3$ (as 14T44)	$6$	$7$	$[12/7]$	$[8/7, 8/7, 8/7, 12/7, 12/7, 12/7]_{7}^{6}$	$t + 1$	$x^{14} + 2 x^{6} + 2 x^{5} + 2$	$[5, 0]$	$[1, 3]$