$p$-adic field search results

Results (1-50 of 795 matches)

 

Label	$n$	Polynomial	$p$	$e$	$f$	$c$	Galois group	$u$	$t$	Visible slopes	Slope content	Ind. of Insep.	Assoc. Inertia
3.9.0.1	$9$	x^9 + 2x^3 + 2x^2 + x + 1	$3$	$1$	$9$	$0$	$C_9$ (as 9T1)	$9$	$1$	$[\ ]$	$[\ ]^{9}$	$[0]$	$[]$
3.9.9.1	$9$	x^9 + 90x^7 - 207x^6 + 540x^5 + 324x^4 + 243x^3 + 324x^2 + 162x + 27	$3$	$3$	$3$	$9$	$S_3\times C_3$ (as 9T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.9.10	$9$	x^9 - 24x^8 + 321x^7 - 117x^6 - 243x^5 + 1062x^4 + 1053x^3 + 135x^2 - 27x + 27	$3$	$3$	$3$	$9$	$(C_3^3:C_3):C_2$ (as 9T22)	$3$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.9.11	$9$	x^9 + 3x + 3	$3$	$9$	$1$	$9$	$(C_3^2:C_8):C_2$ (as 9T19)	$2$	$8$	$[9/8, 9/8]$	$[9/8, 9/8]_{8}^{2}$	$[1, 1, 0]$	$[1]$
3.9.9.12	$9$	x^9 + 6x + 3	$3$	$9$	$1$	$9$	$(C_3^2:C_8):C_2$ (as 9T19)	$2$	$8$	$[9/8, 9/8]$	$[9/8, 9/8]_{8}^{2}$	$[1, 1, 0]$	$[1]$
3.9.9.2	$9$	x^9 - 3x^7 + 9x^6 - 9x^5 - 18x^4 + 81x^3 - 27x^2 - 27x + 27	$3$	$3$	$3$	$9$	$C_3^2 : S_3 $ (as 9T13)	$3$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.9.3	$9$	x^9 - 3x^8 + 126x^7 + 198x^6 + 297x^5 + 567x^4 + 324x^3 + 108x^2 + 81x + 27	$3$	$3$	$3$	$9$	$(C_3^3:C_3):C_2$ (as 9T22)	$3$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.9.4	$9$	x^9 - 24x^8 + 318x^7 - 189x^6 + 1080x^5 + 2826x^4 + 1350x^3 - 108x^2 - 54x + 27	$3$	$3$	$3$	$9$	$(C_3^3:C_3):C_2$ (as 9T22)	$3$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.9.5	$9$	x^9 - 24x^7 + 9x^6 + 216x^5 - 144x^4 + 648x^2 - 216x + 27	$3$	$3$	$3$	$9$	$(C_3^3:C_3):C_2$ (as 9T22)	$3$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.9.6	$9$	x^9 - 6x^8 + 45x^7 + 594x^6 + 99x^5 + 108x^4 - 54x^3 + 27x^2 + 81x + 27	$3$	$3$	$3$	$9$	$S_3\times C_3$ (as 9T4)	$3$	$2$	$[3/2]$	$[3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.9.7	$9$	x^9 - 6x^7 + 9x^6 - 36x^5 - 36x^4 + 459x^3 - 108x^2 - 54x + 27	$3$	$3$	$3$	$9$	$C_3^2 : S_3 $ (as 9T13)	$3$	$2$	$[3/2]$	$[3/2, 3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.9.8	$9$	x^9 + 6x^8 + 114x^7 + 549x^6 + 522x^5 + 495x^4 + 216x^3 + 297x^2 - 108x + 27	$3$	$3$	$3$	$9$	$(C_3^3:C_3):C_2$ (as 9T22)	$3$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.9.9	$9$	x^9 + 9x^6 + 72x^5 - 189x^3 + 216x^2 + 27	$3$	$3$	$3$	$9$	$(C_3^3:C_3):C_2$ (as 9T22)	$3$	$2$	$[3/2]$	$[3/2, 3/2, 3/2]_{2}^{3}$	$[1, 0]$	$[1]$
3.9.10.1	$9$	x^9 + 3x^2 + 3	$3$	$9$	$1$	$10$	$C_3^2:Q_8$ (as 9T14)	$2$	$4$	$[5/4, 5/4]$	$[5/4, 5/4]_{4}^{2}$	$[2, 2, 0]$	$[2]$
3.9.10.2	$9$	x^9 + 6x^2 + 3	$3$	$9$	$1$	$10$	$S_3^2:C_2$ (as 9T16)	$2$	$4$	$[5/4, 5/4]$	$[5/4, 5/4]_{4}^{2}$	$[2, 2, 0]$	$[1]$
3.9.12.1	$9$	x^9 + 18x^8 + 108x^7 + 225x^6 + 108x^5 + 324x^4 + 675x^3 + 4050x^2 - 3861	$3$	$3$	$3$	$12$	$C_3^2$ (as 9T2)	$3$	$1$	$[2]$	$[2]^{3}$	$[2, 0]$	$[1]$
3.9.12.10	$9$	x^9 + 9x^8 + 45x^7 + 90x^6 + 324x^5 + 621x^4 + 594x^3 + 2349x^2 + 2943	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.11	$9$	x^9 - 24x^8 + 324x^7 - 459x^6 + 828x^5 - 972x^4 + 540x^3 - 216x^2 + 432	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.12	$9$	x^9 + 9x^8 + 45x^7 + 54x^6 + 189x^5 + 540x^4 + 297x^3 + 1944x^2 + 3834	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.13	$9$	x^9 - 6x^8 + 144x^7 + 927x^6 + 504x^5 + 4320x^4 + 1971x^3 + 11286x^2 + 17037	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.14	$9$	x^9 - 6x^8 + 144x^7 + 900x^6 + 612x^5 + 3024x^4 + 1080x^3 + 6264x^2 + 3672	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.15	$9$	x^9 - 24x^8 + 216x^7 - 27x^6 + 477x^5 + 1134x^4 + 1026x^3 + 3348x^2 + 6021	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.16	$9$	x^9 + 9x^8 + 27x^7 + 36x^6 + 54x^5 + 81x^4 + 675x^3 + 2025x^2 - 3861	$3$	$3$	$3$	$12$	$S_3\times C_3$ (as 9T4)	$6$	$1$	$[2]$	$[2]^{6}$	$[2, 0]$	$[2]$
3.9.12.17	$9$	x^9 - 6x^8 - 36x^7 + 441x^6 + 126x^5 + 216x^4 + 189x^3 + 1404x^2 - 216	$3$	$3$	$3$	$12$	$C_3^2 : S_3 $ (as 9T13)	$6$	$1$	$[2]$	$[2, 2]^{6}$	$[2, 0]$	$[2]$
3.9.12.18	$9$	x^9 - 12x^8 + 36x^7 + 90x^6 - 342x^5 + 432x^4 + 1971x^3 - 1890x^2 + 17037	$3$	$3$	$3$	$12$	$(C_3^3:C_3):C_2$ (as 9T22)	$6$	$1$	$[2]$	$[2, 2, 2]^{6}$	$[2, 0]$	$[2]$
3.9.12.19	$9$	x^9 + 18x^8 + 180x^7 + 495x^6 + 1188x^5 + 4428x^4 + 1971x^3 + 15066x^2 + 17037	$3$	$3$	$3$	$12$	$(C_3^3:C_3):C_2$ (as 9T22)	$6$	$1$	$[2]$	$[2, 2, 2]^{6}$	$[2, 0]$	$[2]$
3.9.12.2	$9$	x^9 + 18x^8 + 108x^7 + 243x^6 + 324x^5 + 972x^4 + 1269x^3 + 7614x^2 + 15984	$3$	$3$	$3$	$12$	$C_9$ (as 9T1)	$3$	$1$	$[2]$	$[2]^{3}$	$[2, 0]$	$[1]$
3.9.12.20	$9$	x^9 - 12x^8 + 81x^7 - 45x^6 + 117x^5 - 162x^4 + 189x^3 - 270x^2 - 216	$3$	$3$	$3$	$12$	$(C_3^3:C_3):C_2$ (as 9T22)	$6$	$1$	$[2]$	$[2, 2, 2]^{6}$	$[2, 0]$	$[2]$
3.9.12.21	$9$	x^9 + 6x^4 + 3	$3$	$9$	$1$	$12$	$C_3^2:C_4$ (as 9T9)	$2$	$2$	$[3/2, 3/2]$	$[3/2, 3/2]_{2}^{2}$	$[4, 4, 0]$	$[2]$
3.9.12.22	$9$	x^9 + 6x^4 + 6x^3 + 3	$3$	$9$	$1$	$12$	$C_3^2 : C_6$ (as 9T11)	$3$	$2$	$[3/2, 3/2]$	$[3/2, 3/2]_{2}^{3}$	$[4, 3, 0]$	$[3]$
3.9.12.23	$9$	x^9 + 6x^4 + 3x^3 + 3	$3$	$9$	$1$	$12$	$C_3^2 : C_6$ (as 9T11)	$3$	$2$	$[3/2, 3/2]$	$[3/2, 3/2]_{2}^{3}$	$[4, 3, 0]$	$[3]$
3.9.12.24	$9$	x^9 + 3x^4 + 3	$3$	$9$	$1$	$12$	$S_3^2$ (as 9T8)	$2$	$2$	$[3/2, 3/2]$	$[3/2, 3/2]_{2}^{2}$	$[4, 4, 0]$	$[2]$
3.9.12.25	$9$	x^9 + 3x^4 + 6x^3 + 3	$3$	$9$	$1$	$12$	$C_3^2:C_8$ (as 9T15)	$4$	$2$	$[3/2, 3/2]$	$[3/2, 3/2]_{2}^{4}$	$[4, 3, 0]$	$[4]$
3.9.12.26	$9$	x^9 + 3x^4 + 3x^3 + 3	$3$	$9$	$1$	$12$	$C_3^2:C_8$ (as 9T15)	$4$	$2$	$[3/2, 3/2]$	$[3/2, 3/2]_{2}^{4}$	$[4, 3, 0]$	$[4]$
3.9.12.3	$9$	x^9 + 18x^8 + 108x^7 + 153x^6 - 756x^5 - 2268x^4 + 891x^3 + 5346x^2 + 9099	$3$	$3$	$3$	$12$	$C_9$ (as 9T1)	$3$	$1$	$[2]$	$[2]^{3}$	$[2, 0]$	$[1]$
3.9.12.4	$9$	x^9 + 6x^8 + 45x^7 + 252x^6 + 144x^5 + 540x^4 + 432x^3 + 864x^2 + 1728	$3$	$3$	$3$	$12$	$C_3^2:C_3$ (as 9T7)	$3$	$1$	$[2]$	$[2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.5	$9$	x^9 + 6x^8 + 126x^7 + 468x^6 + 630x^5 + 1674x^4 + 675x^3 - 108x^2 - 3861	$3$	$3$	$3$	$12$	$C_9:C_3$ (as 9T6)	$3$	$1$	$[2]$	$[2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.6	$9$	x^9 - 3x^8 - 9x^7 + 63x^6 + 63x^5 + 54x^4 + 189x^3 + 702x^2 - 216	$3$	$3$	$3$	$12$	$C_9:C_3$ (as 9T6)	$3$	$1$	$[2]$	$[2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.7	$9$	x^9 - 6x^8 + 36x^7 + 621x^6 + 477x^5 + 3996x^4 + 1026x^3 + 9504x^2 + 6021	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.8	$9$	x^9 - 24x^8 + 324x^7 - 405x^6 - 36x^5 + 4860x^4 + 540x^3 + 6912x^2 + 7236	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.12.9	$9$	x^9 + 9x^8 + 45x^7 + 117x^6 + 486x^5 + 1026x^4 + 1485x^3 + 5994x^2 + 11934	$3$	$3$	$3$	$12$	$C_3 \wr C_3 $ (as 9T17)	$3$	$1$	$[2]$	$[2, 2, 2]^{3}$	$[2, 0]$	$[1]$
3.9.13.1	$9$	x^9 + 6x^5 + 3	$3$	$9$	$1$	$13$	$(C_3^2:C_8):C_2$ (as 9T19)	$2$	$8$	$[13/8, 13/8]$	$[13/8, 13/8]_{8}^{2}$	$[5, 5, 0]$	$[1]$
3.9.13.10	$9$	x^9 + 6x^6 + 3x^5 + 3x^3 + 3	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$3$	$2$	$[3/2, 5/3]$	$[3/2, 3/2, 5/3]_{2}^{3}$	$[5, 3, 0]$	$[1, 1]$
3.9.13.2	$9$	x^9 + 6x^5 + 3x^3 + 3	$3$	$9$	$1$	$13$	$C_3^2 : D_{6} $ (as 9T18)	$2$	$2$	$[3/2, 5/3]$	$[3/2, 3/2, 5/3]_{2}^{2}$	$[5, 3, 0]$	$[2, 1]$
3.9.13.3	$9$	x^9 + 3x^6 + 6x^5 + 6x^3 + 3	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$3$	$2$	$[3/2, 5/3]$	$[3/2, 3/2, 5/3]_{2}^{3}$	$[5, 3, 0]$	$[1, 1]$
3.9.13.4	$9$	x^9 + 6x^5 + 6x^3 + 3	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$3$	$2$	$[3/2, 5/3]$	$[3/2, 3/2, 5/3]_{2}^{3}$	$[5, 3, 0]$	$[1, 1]$
3.9.13.5	$9$	x^9 + 6x^6 + 6x^5 + 6x^3 + 3	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$3$	$2$	$[3/2, 5/3]$	$[3/2, 3/2, 5/3]_{2}^{3}$	$[5, 3, 0]$	$[1, 1]$
3.9.13.6	$9$	x^9 + 3x^5 + 3	$3$	$9$	$1$	$13$	$(C_3^2:C_8):C_2$ (as 9T19)	$2$	$8$	$[13/8, 13/8]$	$[13/8, 13/8]_{8}^{2}$	$[5, 5, 0]$	$[1]$
3.9.13.7	$9$	x^9 + 3x^5 + 6x^3 + 3	$3$	$9$	$1$	$13$	$C_3^2 : D_{6} $ (as 9T18)	$2$	$2$	$[3/2, 5/3]$	$[3/2, 3/2, 5/3]_{2}^{2}$	$[5, 3, 0]$	$[2, 1]$
3.9.13.8	$9$	x^9 + 3x^5 + 3x^3 + 3	$3$	$9$	$1$	$13$	$C_3 \wr S_3 $ (as 9T20)	$3$	$2$	$[3/2, 5/3]$	$[3/2, 3/2, 5/3]_{2}^{3}$	$[5, 3, 0]$	$[1, 1]$