$p$-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
23.12.0.1	$12$	x^12 + 21x^7 + 21x^6 + 15x^5 + 14x^4 + 12x^3 + 18x^2 + 12x + 5	$23$	$1$	$12$	$0$	$C_{12}$ (as 12T1)	$12$	$1$	$[\ ]$	$[\ ]^{12}$	$[0]$	$[]$
23.12.6.1	$12$	x^12 + 140x^10 + 18x^9 + 8092x^8 + 20x^7 + 244001x^6 - 56140x^5 + 4059563x^4 - 1721304x^3 + 36312468x^2 - 14694000x + 141161628	$23$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
23.12.6.2	$12$	x^12 + 529x^8 - 109503x^6 + 2518569x^4 - 6436343x^2 + 740179445	$23$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
23.12.8.1	$12$	x^12 + 9x^10 + 149x^9 + 42x^8 + 342x^7 - 3492x^6 - 3195x^5 - 6891x^4 - 80901x^3 + 124182x^2 - 232623x + 1674962	$23$	$3$	$4$	$8$	$C_3 : C_4$ (as 12T5)	$4$	$3$	$[\ ]$	$[\ ]_{3}^{4}$	$[0]$	$[1]$
23.12.8.2	$12$	x^12 - 138x^9 + 10051x^6 + 4027277x^3 + 6996025	$23$	$3$	$4$	$8$	$C_3\times (C_3 : C_4)$ (as 12T19)	$12$	$3$	$[\ ]$	$[\ ]_{3}^{12}$	$[0]$	$[1]$
23.12.9.1	$12$	x^12 + 8x^10 + 72x^9 + 93x^8 + 432x^7 + 1608x^6 - 19008x^5 + 10115x^4 + 20592x^3 + 219376x^2 + 154296x + 181359	$23$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$[0]$	$[2]$
23.12.9.2	$12$	x^12 + 1058x^4 - 219006	$23$	$4$	$3$	$9$	$D_4 \times C_3$ (as 12T14)	$6$	$4$	$[\ ]$	$[\ ]_{4}^{6}$	$[0]$	$[2]$
23.12.10.1	$12$	x^12 + 126x^11 + 6645x^10 + 188370x^9 + 3049890x^8 + 27314406x^7 + 115933067x^6 + 136574928x^5 + 76395945x^4 + 27661410x^3 + 68223420x^2 + 532411488x + 1840721472	$23$	$6$	$2$	$10$	$D_6$ (as 12T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
23.12.10.2	$12$	x^12 - 138x^6 - 217948	$23$	$6$	$2$	$10$	$C_6\times S_3$ (as 12T18)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$[0]$	$[1]$
23.12.10.3	$12$	x^12 - 10028x^6 - 1807593	$23$	$6$	$2$	$10$	$C_3 : C_4$ (as 12T5)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
23.12.10.4	$12$	x^12 - 483x^6 + 2645	$23$	$6$	$2$	$10$	$C_3\times (C_3 : C_4)$ (as 12T19)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$[0]$	$[1]$
23.12.11.1	$12$	x^12 + 23	$23$	$12$	$1$	$11$	$D_{12}$ (as 12T12)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
23.12.11.2	$12$	x^12 + 115	$23$	$12$	$1$	$11$	$D_{12}$ (as 12T12)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$