pp-adic field search results

Results (17 matches)

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Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Unram. Ext.	Eisen. Poly.	Ind. of Insep.	Assoc. Inertia
5.12.0.1	$12$	$x^{12} + x^{7} + x^{6} + 4 x^{4} + 4 x^{3} + 3 x^{2} + 2 x + 2$	$5$	$1$	$12$	$0$	$C_{12}$ (as 12T1)	$12$	$1$	$[\ ]$	$[\ ]^{12}$	$t^{12} + t^{7} + t^{6} + 4 t^{4} + 4 t^{3} + 3 t^{2} + 2 t + 2$	$x - 5$	$[0]$	$[\ ]$
5.12.6.1	$12$	$x^{12} + 120 x^{11} + 6032 x^{10} + 163208 x^{9} + 2529528 x^{8} + 21853448 x^{7} + 92223962 x^{6} + 138649448 x^{5} + 223472880 x^{4} + 401794296 x^{3} + 295909124 x^{2} + 118616440 x + 126881009$	$5$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$t^{6} + t^{4} + 4 t^{3} + t^{2} + 2$	$x^{2} + 20 x + 5$	$[0]$	$[1]$
5.12.6.2	$12$	$x^{12} + 25 x^{8} - 500 x^{6} + 625 x^{4} + 31250$	$5$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$t^{6} + t^{4} + 4 t^{3} + t^{2} + 2$	$x^{2} + 5 t$	$[0]$	$[1]$
5.12.8.1	$12$	$x^{12} + 12 x^{10} + 32 x^{9} + 54 x^{8} + 96 x^{7} - 50 x^{6} + 240 x^{5} - 360 x^{4} - 884 x^{3} + 4044 x^{2} - 3912 x + 4173$	$5$	$3$	$4$	$8$	$C_3 : C_4$ (as 12T5)	$4$	$3$	$[\ ]$	$[\ ]_{3}^{4}$	$t^{4} + 4 t^{2} + 4 t + 2$	$x^{3} + 5$	$[0]$	$[1]$
5.12.8.2	$12$	$x^{12} + 100 x^{6} - 500 x^{3} + 1250$	$5$	$3$	$4$	$8$	$C_3\times (C_3 : C_4)$ (as 12T19)	$12$	$3$	$[\ ]$	$[\ ]_{3}^{12}$	$t^{4} + 4 t^{2} + 4 t + 2$	$x^{3} + 5 t$	$[0]$	$[1]$
5.12.9.1	$12$	$x^{12} - 30 x^{8} + 225 x^{4} + 1125$	$5$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$t^{3} + 3 t + 3$	$x^{4} + 5 t^{2}$	$[0]$	$[1]$
5.12.9.2	$12$	$x^{12} + 12 x^{10} + 12 x^{9} + 69 x^{8} + 108 x^{7} + 42 x^{6} - 396 x^{5} + 840 x^{4} + 252 x^{3} + 1476 x^{2} + 684 x + 1601$	$5$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$t^{3} + 3 t + 3$	$x^{4} + 5$	$[0]$	$[1]$
5.12.9.3	$12$	$x^{12} + 75 x^{4} - 375$	$5$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$t^{3} + 3 t + 3$	$x^{4} + 5 t$	$[0]$	$[1]$
5.12.9.4	$12$	$x^{12} + 30 x^{8} + 600 x^{4} + 1000$	$5$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$t^{3} + 3 t + 3$	$x^{4} + 10 t + 10$	$[0]$	$[1]$
5.12.10.1	$12$	$x^{12} + 20 x^{7} + 10 x^{6} + 50 x^{2} + 100 x + 25$	$5$	$6$	$2$	$10$	$D_6$ (as 12T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$t^{2} + 4 t + 2$	$x^{6} + \left(5 t + 20\right) x + 5$	$[0]$	$[1]$
5.12.10.2	$12$	$x^{12} - 20 x^{6} - 100$	$5$	$6$	$2$	$10$	$C_6\times S_3$ (as 12T18)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$t^{2} + 4 t + 2$	$x^{6} + 10 t + 10$	$[0]$	$[1]$
5.12.10.3	$12$	$x^{12} - 50 x^{6} - 175$	$5$	$6$	$2$	$10$	$C_3 : C_4$ (as 12T5)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$t^{2} + 4 t + 2$	$x^{6} + 20 t + 15$	$[0]$	$[1]$
5.12.10.4	$12$	$x^{12} - 70 x^{6} + 425$	$5$	$6$	$2$	$10$	$C_3\times (C_3 : C_4)$ (as 12T19)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$t^{2} + 4 t + 2$	$x^{6} + 20 t + 5$	$[0]$	$[1]$
5.12.11.1	$12$	$x^{12} + 20$	$5$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$t + 3$	$x^{12} + 20$	$[0]$	$[2]$
5.12.11.2	$12$	$x^{12} + 5$	$5$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$t + 3$	$x^{12} + 5$	$[0]$	$[2]$
5.12.11.3	$12$	$x^{12} + 10$	$5$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$t + 3$	$x^{12} + 10$	$[0]$	$[2]$
5.12.11.4	$12$	$x^{12} + 15$	$5$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$t + 3$	$x^{12} + 15$	$[0]$	$[2]$

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