$p$-adic field search results

Results (5 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
2.12.12.32	$12$	$x^{12} - 4 x^{10} - 4 x^{9} + 26 x^{8} + 40 x^{7} - 4 x^{6} - 40 x^{5} + 28 x^{4} + 72 x^{3} + 24 x^{2} - 16 x + 8$	$2$	$4$	$3$	$12$	$A_4\wr C_2$ (as 12T129)	$6$	$3$	$[4/3, 4/3]$	$[4/3, 4/3, 4/3, 4/3]_{3}^{6}$	$t^{3} + t + 1$	$x^{4} + \left(2 t^{2} + 2 t\right) x^{2} + \left(2 t^{2} + 2 t\right) x + 2$	$[1, 1, 0]$	$[1]$
2.12.24.205	$12$	$x^{12} + 12 x^{11} + 56 x^{10} + 72 x^{9} + 82 x^{8} + 352 x^{7} + 432 x^{6} + 64 x^{5} + 620 x^{4} + 976 x^{3} - 192 x^{2} - 288 x + 216$	$2$	$4$	$3$	$24$	$A_4\wr C_2$ (as 12T129)	$6$	$3$	$[8/3, 8/3]$	$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$	$t^{3} + t + 1$	$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 4 t^{2} x + 6$	$[5, 4, 0]$	$[1]$
2.12.24.217	$12$	$x^{12} - 8 x^{11} + 28 x^{10} + 166 x^{8} - 176 x^{7} + 288 x^{6} + 96 x^{5} + 284 x^{4} + 128 x^{3} - 48 x^{2} - 128 x - 24$	$2$	$4$	$3$	$24$	$A_4\wr C_2$ (as 12T129)	$6$	$3$	$[8/3, 8/3]$	$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$	$t^{3} + t + 1$	$x^{4} + 4 t^{2} x^{3} + 4 x^{2} + 4 t x + 4 t + 2$	$[5, 4, 0]$	$[1]$
2.12.24.24	$12$	$x^{12} + 12 x^{11} + 40 x^{10} - 8 x^{9} - 166 x^{8} + 96 x^{7} + 560 x^{6} + 176 x^{5} + 316 x^{4} + 784 x^{3} + 640 x^{2} + 320 x + 88$	$2$	$4$	$3$	$24$	$A_4\wr C_2$ (as 12T129)	$6$	$3$	$[8/3, 8/3]$	$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$	$t^{3} + t + 1$	$x^{4} + 4 x^{3} + 4 t^{2} x^{2} + \left(4 t^{2} + 4 t\right) x + 4 t^{2} + 6$	$[5, 4, 0]$	$[1]$
2.12.24.87	$12$	$x^{12} + 4 x^{10} - 8 x^{9} + 82 x^{8} + 16 x^{7} + 256 x^{6} + 160 x^{5} + 684 x^{4} + 160 x^{3} + 240 x^{2} - 288 x + 216$	$2$	$4$	$3$	$24$	$A_4\wr C_2$ (as 12T129)	$6$	$3$	$[8/3, 8/3]$	$[8/3, 8/3, 8/3, 8/3]_{3}^{6}$	$t^{3} + t + 1$	$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{2} + 4 t^{2} x + 6$	$[5, 4, 0]$	$[1]$