$p$-adic field search results

Results (7 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
2.6.6.2	$6$	$x^{6} + 6 x^{5} + 14 x^{4} + 24 x^{3} + 44 x^{2} + 8 x + 72$	$2$	$2$	$3$	$6$	$A_4\times C_2$ (as 6T6)	$6$	$1$	$[2]$	$[2, 2]^{6}$	$t^{3} + t + 1$	$x^{2} + \left(2 t + 2\right) x + 4 t^{2} + 2$	$[1, 0]$	$[1]$
2.6.6.4	$6$	$x^{6} - 4 x^{5} + 14 x^{4} - 24 x^{3} + 100 x^{2} + 48 x + 88$	$2$	$2$	$3$	$6$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + t + 1$	$x^{2} + 2 t^{2} x + 4 t^{2} + 6$	$[1, 0]$	$[1]$
2.6.6.6	$6$	$x^{6} - 4 x^{5} + 30 x^{4} - 16 x^{3} + 164 x^{2} + 160 x + 88$	$2$	$2$	$3$	$6$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(2 t^{2} + 2 t\right) x + 4 t^{2} + 6$	$[1, 0]$	$[1]$
2.6.9.2	$6$	$x^{6} + 4 x^{5} - 10 x^{4} + 160 x^{3} + 1212 x^{2} + 2160 x - 1048$	$2$	$2$	$3$	$9$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 12 t + 2$	$[2, 0]$	$[1]$
2.6.9.4	$6$	$x^{6} + 4 x^{5} + 14 x^{4} + 224 x^{3} + 1244 x^{2} + 3184 x + 2376$	$2$	$2$	$3$	$9$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 12 t + 10$	$[2, 0]$	$[1]$
2.6.9.6	$6$	$x^{6} - 8 x^{5} + 86 x^{4} + 96 x^{3} + 860 x^{2} + 2976 x + 2728$	$2$	$2$	$3$	$9$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 4 t + 10$	$[2, 0]$	$[1]$
2.6.9.8	$6$	$x^{6} - 8 x^{5} + 62 x^{4} + 224 x^{3} + 316 x^{2} + 1184 x + 1608$	$2$	$2$	$3$	$9$	$A_4\times C_2$ (as 6T6)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 4 t + 2$	$[2, 0]$	$[1]$