$p$-adic field search results

Results (17 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
17.12.0.1	$12$	x^12 + x^8 + 4x^7 + 14x^6 + 14x^5 + 13x^4 + 6x^3 + 14x^2 + 9x + 3	$17$	$1$	$12$	$0$	$C_{12}$ (as 12T1)	$12$	$1$	$[\ ]$	$[\ ]^{12}$	$[0]$	$[]$
17.12.6.1	$12$	x^12 + 918x^11 + 351241x^10 + 71712630x^9 + 8244584136x^8 + 506874732756x^7 + 13125344775560x^6 + 9625198256031x^5 + 28457943732288x^4 + 16844354225613x^3 + 132306217741765x^2 + 68598705820311x + 44162739951115	$17$	$2$	$6$	$6$	$C_6\times C_2$ (as 12T2)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
17.12.6.2	$12$	x^12 + 578x^8 + 835210x^4 - 4259571x^2 + 72412707	$17$	$2$	$6$	$6$	$C_{12}$ (as 12T1)	$6$	$2$	$[\ ]$	$[\ ]_{2}^{6}$	$[0]$	$[1]$
17.12.8.1	$12$	x^12 + 225x^10 + 98x^9 + 17904x^8 + 10824x^7 + 611647x^6 + 498390x^5 + 8494833x^4 + 11764900x^3 + 38205036x^2 + 73669974x + 36476587	$17$	$3$	$4$	$8$	$C_3 : C_4$ (as 12T5)	$4$	$3$	$[\ ]$	$[\ ]_{3}^{4}$	$[0]$	$[1]$
17.12.8.2	$12$	x^12 + 2023x^6 - 49130x^3 + 250563	$17$	$3$	$4$	$8$	$C_3\times (C_3 : C_4)$ (as 12T19)	$12$	$3$	$[\ ]$	$[\ ]_{3}^{12}$	$[0]$	$[1]$
17.12.9.1	$12$	x^12 + 4x^10 + 56x^9 + 57x^8 + 168x^7 + 1044x^6 - 11256x^5 + 3356x^4 + 10080x^3 + 97736x^2 + 58576x + 57252	$17$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$[0]$	$[1]$
17.12.9.2	$12$	x^12 - 34x^8 + 289x^4 + 962948	$17$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$[0]$	$[1]$
17.12.9.3	$12$	x^12 + 289x^4 - 68782	$17$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$[0]$	$[1]$
17.12.9.4	$12$	x^12 + 153x^8 + 81787x^4 - 277825237	$17$	$4$	$3$	$9$	$C_{12}$ (as 12T1)	$3$	$4$	$[\ ]$	$[\ ]_{4}^{3}$	$[0]$	$[1]$
17.12.10.1	$12$	x^12 + 96x^11 + 3858x^10 + 83360x^9 + 1029255x^8 + 7037376x^7 + 22883390x^6 + 21113760x^5 + 9327045x^4 + 3594400x^3 + 16245408x^2 + 100784640x + 265511268	$17$	$6$	$2$	$10$	$D_6$ (as 12T3)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
17.12.10.2	$12$	x^12 - 3060x^6 - 197676	$17$	$6$	$2$	$10$	$C_6\times S_3$ (as 12T18)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$[0]$	$[1]$
17.12.10.3	$12$	x^12 - 3604x^6 - 719321	$17$	$6$	$2$	$10$	$C_3 : C_4$ (as 12T5)	$2$	$6$	$[\ ]$	$[\ ]_{6}^{2}$	$[0]$	$[1]$
17.12.10.4	$12$	x^12 + 238x^6 - 3468	$17$	$6$	$2$	$10$	$C_3\times (C_3 : C_4)$ (as 12T19)	$6$	$6$	$[\ ]$	$[\ ]_{6}^{6}$	$[0]$	$[1]$
17.12.11.1	$12$	x^12 + 17	$17$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
17.12.11.2	$12$	x^12 + 34	$17$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
17.12.11.3	$12$	x^12 + 51	$17$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$
17.12.11.4	$12$	x^12 + 102	$17$	$12$	$1$	$11$	$S_3 \times C_4$ (as 12T11)	$2$	$12$	$[\ ]$	$[\ ]_{12}^{2}$	$[0]$	$[2]$