$p$-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
2.6.9.1	$6$	$x^{6} + 44 x^{4} + 2 x^{3} + 589 x^{2} - 82 x + 2367$	$2$	$2$	$3$	$9$	$C_6$ (as 6T1)	$3$	$1$	$[3]$	$[3]^{3}$	$t^{3} + t + 1$	$x^{2} + 14$	$[2, 0]$	$[1]$
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)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 12 t + 2$	$[2, 0]$	$[1]$
2.6.9.3	$6$	$x^{6} + 12 x^{5} + 86 x^{4} + 352 x^{3} + 892 x^{2} + 1552 x + 1384$	$2$	$2$	$3$	$9$	$C_6$ (as 6T1)	$3$	$1$	$[3]$	$[3]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(4 t + 4\right) x + 4 t^{2} + 8 t + 10$	$[2, 0]$	$[1]$
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)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 12 t + 10$	$[2, 0]$	$[1]$
2.6.9.5	$6$	$x^{6} + 12 x^{5} + 68 x^{4} + 226 x^{3} + 457 x^{2} + 514 x + 243$	$2$	$2$	$3$	$9$	$C_6$ (as 6T1)	$3$	$1$	$[3]$	$[3]^{3}$	$t^{3} + t + 1$	$x^{2} + 4 x + 6$	$[2, 0]$	$[1]$
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)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 4 t + 10$	$[2, 0]$	$[1]$
2.6.9.7	$6$	$x^{6} + 32 x^{4} + 2 x^{3} + 301 x^{2} - 58 x + 811$	$2$	$2$	$3$	$9$	$C_6$ (as 6T1)	$3$	$1$	$[3]$	$[3]^{3}$	$t^{3} + t + 1$	$x^{2} + 10$	$[2, 0]$	$[1]$
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)	$3$	$1$	$[3]$	$[2, 2, 3]^{3}$	$t^{3} + t + 1$	$x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 4 t + 2$	$[2, 0]$	$[1]$