$p$-adic field search results

Results (18 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
2.12.18.69	$12$	$x^{12} + 2 x^{11} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 2$	$2$	$12$	$1$	$18$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[4/3, 2]$	$[4/3, 4/3, 5/3, 5/3, 2]_{3}^{2}$	$t + 1$	$x^{12} + 2 x^{11} + 2 x^{7} + 2 x^{4} + 2 x^{2} + 2$	$[7, 2, 0]$	$[1, 1, 2]$
2.12.22.133	$12$	$x^{12} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 6$	$2$	$12$	$1$	$22$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[4/3, 8/3]$	$[4/3, 4/3, 2, 8/3, 8/3]_{3}^{2}$	$t + 1$	$x^{12} + 2 x^{11} + 4 x^{7} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 6$	$[11, 2, 0]$	$[1, 1, 2]$
2.12.24.387	$12$	$x^{12} + 4 x^{10} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 4 x + 10$	$2$	$12$	$1$	$24$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[4/3, 3]$	$[4/3, 4/3, 5/3, 5/3, 3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{10} + 6 x^{6} + 4 x^{5} + 6 x^{4} + 2 x^{2} + 4 x + 10$	$[13, 2, 0]$	$[1, 1, 2]$
2.12.24.421	$12$	$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 6 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$	$2$	$12$	$1$	$24$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[4/3, 3]$	$[4/3, 4/3, 5/3, 5/3, 3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 4 x^{10} + 4 x^{9} + 4 x^{7} + 6 x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 2$	$[13, 2, 0]$	$[1, 1, 2]$
2.12.24.433	$12$	$x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 4 x + 10$	$2$	$12$	$1$	$24$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[4/3, 3]$	$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{8} + 4 x^{6} + 4 x^{5} + 2 x^{4} + 6 x^{2} + 4 x + 10$	$[13, 2, 0]$	$[1, 1, 2]$
2.12.24.441	$12$	$x^{12} + 4 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 6 x^{2} + 4 x + 2$	$2$	$12$	$1$	$24$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[4/3, 3]$	$[4/3, 4/3, 8/3, 8/3, 3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 2 x^{10} + 2 x^{8} + 4 x^{7} + 4 x^{6} + 4 x^{5} + 6 x^{4} + 6 x^{2} + 4 x + 2$	$[13, 2, 0]$	$[1, 1, 2]$
2.12.32.11	$12$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{5} + 12 x^{2} + 8 x + 10$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{5} + 12 x^{2} + 8 x + 10$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.144	$12$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{8} + 8 x^{6} + 12 x^{4} + 8 x^{3} + 12 x^{2} + 8 x + 2$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.162	$12$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 4 x^{2} + 2$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{7} + 8 x^{5} + 12 x^{4} + 4 x^{2} + 2$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.192	$12$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{4} + 12 x^{2} + 8 x + 10$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{4} + 12 x^{2} + 8 x + 10$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.208	$12$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{5} + 12 x^{4} + 4 x^{2} + 2$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 8 x^{5} + 12 x^{4} + 4 x^{2} + 2$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.316	$12$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{7} + 12 x^{2} + 8 x + 10$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{7} + 12 x^{2} + 8 x + 10$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.32	$12$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{2} + 8 x + 10$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{8} + 8 x^{7} + 8 x^{5} + 12 x^{2} + 8 x + 10$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.485	$12$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{8} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 10$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{8} + 8 x^{4} + 8 x^{3} + 4 x^{2} + 10$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.487	$12$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{7} + 4 x^{2} + 2$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[2, 8/3, 8/3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 4 x^{8} + 8 x^{7} + 4 x^{2} + 2$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.488	$12$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{8} + 12 x^{2} + 8 x + 10$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 12 x^{8} + 12 x^{2} + 8 x + 10$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.505	$12$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{5} + 4 x^{4} + 12 x^{2} + 8 x + 10$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 2 x^{10} + 4 x^{9} + 8 x^{5} + 4 x^{4} + 12 x^{2} + 8 x + 10$	$[21, 10, 0]$	$[1, 1, 2]$
2.12.32.74	$12$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$	$2$	$12$	$1$	$32$	$C_4^2:D_6$ (as 12T96)	$2$	$3$	$[8/3, 11/3]$	$[8/3, 8/3, 3, 11/3, 11/3]_{3}^{2}$	$t + 1$	$x^{12} + 4 x^{11} + 6 x^{10} + 4 x^{9} + 12 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 2$	$[21, 10, 0]$	$[1, 1, 2]$