$p$-adic field search results

Results (13 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
11.12.0.1	$12$	x^12 + x^8 + x^7 + 4x^6 + 2x^5 + 5x^4 + 5x^3 + 6x^2 + 5x + 2	$11$	$1$	$12$	$0$	$C_{12}$ (as 12T1)	$12$	$1$	$[\ ]$	$[\ ]^{12}$	$[0]$	$[]$
11.12.6.1	$12$	x^12 + 72x^10 + 8x^9 + 2034x^8 + 38x^7 + 27996x^6 - 6312x^5 + 196025x^4 - 84710x^3 + 695581x^2 - 235284x + 1080083	$11$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
11.12.6.2	$12$	x^12 + 363x^8 - 5324x^6 + 87846x^4 - 1127357x^2 + 3543122	$11$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
11.12.8.1	$12$	x^12 + 24x^10 + 74x^9 + 198x^8 + 480x^7 - 346x^6 + 5208x^5 - 3276x^4 - 856x^3 + 53628x^2 - 74328x + 152743	$11$	$3$	$4$	$8$	$C_3 : C_4$ (as 12T5)	$4$	$3$	$[\ ]$	$[\ ]_{3}^{4}$	$[0]$	$[1]$
11.12.8.2	$12$	x^12 - 176x^9 + 8228x^6 + 90508x^3 + 58564	$11$	$3$	$4$	$8$	$C_3\times (C_3 : C_4)$ (as 12T19)	$12$	$3$	$[\ ]$	$[\ ]_{3}^{12}$	$[0]$	$[1]$
11.12.9.1	$12$	x^12 + 8x^10 + 36x^9 + 57x^8 + 216x^7 + 342x^6 - 4320x^5 + 2675x^4 + 2412x^3 + 26122x^2 + 17316x + 16164	$11$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$[0]$	$[2]$
11.12.9.2	$12$	x^12 + 242x^4 - 11979	$11$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$[0]$	$[2]$
11.12.10.1	$12$	x^12 + 42x^11 + 747x^10 + 7280x^9 + 41955x^8 + 143682x^7 + 279531x^6 + 287826x^5 + 175245x^4 + 124460x^3 + 344757x^2 + 893466x + 996620	$11$	$6$	$2$	$10$	$D_6$ (as 12T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
11.12.10.2	$12$	x^12 - 198x^6 - 10043	$11$	$6$	$2$	$10$	$C_6\times S_3$ (as 12T18)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$[0]$	$[1]$
11.12.10.3	$12$	x^12 - 165x^6 - 4356	$11$	$6$	$2$	$10$	$C_3 : C_4$ (as 12T5)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
11.12.10.4	$12$	x^12 - 704x^6 - 121	$11$	$6$	$2$	$10$	$C_3\times (C_3 : C_4)$ (as 12T19)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$[0]$	$[1]$
11.12.11.1	$12$	x^12 + 11	$11$	$12$	$1$	$11$	$D_{12}$ (as 12T12)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
11.12.11.2	$12$	x^12 + 22	$11$	$12$	$1$	$11$	$D_{12}$ (as 12T12)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$