Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Ind. of Insep. |
Assoc. Inertia |
3.9.0.1 |
$9$ |
x9 + 2x3 + 2x2 + x + 1 |
$3$ |
$1$ |
$9$ |
$0$ |
$C_9$ (as 9T1) |
$9$ |
$1$ |
$[\ ]$ |
$[\ ]^{9}$ |
$[0]$ |
$[]$ |
3.9.9.1 |
$9$ |
x9 + 90x7 - 207x6 + 540x5 + 324x4 + 243x3 + 324x2 + 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 |
$9$ |
x9 - 24x8 + 321x7 - 117x6 - 243x5 + 1062x4 + 1053x3 + 135x2 - 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 |
$9$ |
x9 + 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 |
$9$ |
x9 + 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 |
$9$ |
x9 - 3x7 + 9x6 - 9x5 - 18x4 + 81x3 - 27x2 - 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 |
$9$ |
x9 - 3x8 + 126x7 + 198x6 + 297x5 + 567x4 + 324x3 + 108x2 + 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 |
$9$ |
x9 - 24x8 + 318x7 - 189x6 + 1080x5 + 2826x4 + 1350x3 - 108x2 - 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 |
$9$ |
x9 - 24x7 + 9x6 + 216x5 - 144x4 + 648x2 - 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 |
$9$ |
x9 - 6x8 + 45x7 + 594x6 + 99x5 + 108x4 - 54x3 + 27x2 + 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 |
$9$ |
x9 - 6x7 + 9x6 - 36x5 - 36x4 + 459x3 - 108x2 - 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 |
$9$ |
x9 + 6x8 + 114x7 + 549x6 + 522x5 + 495x4 + 216x3 + 297x2 - 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 |
$9$ |
x9 + 9x6 + 72x5 - 189x3 + 216x2 + 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 |
$9$ |
x9 + 3x2 + 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 |
$9$ |
x9 + 6x2 + 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 |
$9$ |
x9 + 18x8 + 108x7 + 225x6 + 108x5 + 324x4 + 675x3 + 4050x2 - 3861 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2$ (as 9T2) |
$3$ |
$1$ |
$[2]$ |
$[2]^{3}$ |
$[2, 0]$ |
$[1]$ |
3.9.12.10 |
$9$ |
x9 + 9x8 + 45x7 + 90x6 + 324x5 + 621x4 + 594x3 + 2349x2 + 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 |
$9$ |
x9 - 24x8 + 324x7 - 459x6 + 828x5 - 972x4 + 540x3 - 216x2 + 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 |
$9$ |
x9 + 9x8 + 45x7 + 54x6 + 189x5 + 540x4 + 297x3 + 1944x2 + 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 |
$9$ |
x9 - 6x8 + 144x7 + 927x6 + 504x5 + 4320x4 + 1971x3 + 11286x2 + 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 |
$9$ |
x9 - 6x8 + 144x7 + 900x6 + 612x5 + 3024x4 + 1080x3 + 6264x2 + 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 |
$9$ |
x9 - 24x8 + 216x7 - 27x6 + 477x5 + 1134x4 + 1026x3 + 3348x2 + 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 |
$9$ |
x9 + 9x8 + 27x7 + 36x6 + 54x5 + 81x4 + 675x3 + 2025x2 - 3861 |
$3$ |
$3$ |
$3$ |
$12$ |
$S_3\times C_3$ (as 9T4) |
$6$ |
$1$ |
$[2]$ |
$[2]^{6}$ |
$[2, 0]$ |
$[2]$ |
3.9.12.17 |
$9$ |
x9 - 6x8 - 36x7 + 441x6 + 126x5 + 216x4 + 189x3 + 1404x2 - 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 |
$9$ |
x9 - 12x8 + 36x7 + 90x6 - 342x5 + 432x4 + 1971x3 - 1890x2 + 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 |
$9$ |
x9 + 18x8 + 180x7 + 495x6 + 1188x5 + 4428x4 + 1971x3 + 15066x2 + 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 |
$9$ |
x9 + 18x8 + 108x7 + 243x6 + 324x5 + 972x4 + 1269x3 + 7614x2 + 15984 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]$ |
$[2]^{3}$ |
$[2, 0]$ |
$[1]$ |
3.9.12.20 |
$9$ |
x9 - 12x8 + 81x7 - 45x6 + 117x5 - 162x4 + 189x3 - 270x2 - 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 |
$9$ |
x9 + 6x4 + 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 |
$9$ |
x9 + 6x4 + 6x3 + 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 |
$9$ |
x9 + 6x4 + 3x3 + 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 |
$9$ |
x9 + 3x4 + 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 |
$9$ |
x9 + 3x4 + 6x3 + 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 |
$9$ |
x9 + 3x4 + 3x3 + 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 |
$9$ |
x9 + 18x8 + 108x7 + 153x6 - 756x5 - 2268x4 + 891x3 + 5346x2 + 9099 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]$ |
$[2]^{3}$ |
$[2, 0]$ |
$[1]$ |
3.9.12.4 |
$9$ |
x9 + 6x8 + 45x7 + 252x6 + 144x5 + 540x4 + 432x3 + 864x2 + 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 |
$9$ |
x9 + 6x8 + 126x7 + 468x6 + 630x5 + 1674x4 + 675x3 - 108x2 - 3861 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9:C_3$ (as 9T6) |
$3$ |
$1$ |
$[2]$ |
$[2, 2]^{3}$ |
$[2, 0]$ |
$[1]$ |
3.9.12.6 |
$9$ |
x9 - 3x8 - 9x7 + 63x6 + 63x5 + 54x4 + 189x3 + 702x2 - 216 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9:C_3$ (as 9T6) |
$3$ |
$1$ |
$[2]$ |
$[2, 2]^{3}$ |
$[2, 0]$ |
$[1]$ |
3.9.12.7 |
$9$ |
x9 - 6x8 + 36x7 + 621x6 + 477x5 + 3996x4 + 1026x3 + 9504x2 + 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 |
$9$ |
x9 - 24x8 + 324x7 - 405x6 - 36x5 + 4860x4 + 540x3 + 6912x2 + 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 |
$9$ |
x9 + 9x8 + 45x7 + 117x6 + 486x5 + 1026x4 + 1485x3 + 5994x2 + 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 |
$9$ |
x9 + 6x5 + 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 |
$9$ |
x9 + 6x6 + 3x5 + 3x3 + 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 |
$9$ |
x9 + 6x5 + 3x3 + 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 |
$9$ |
x9 + 3x6 + 6x5 + 6x3 + 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 |
$9$ |
x9 + 6x5 + 6x3 + 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 |
$9$ |
x9 + 6x6 + 6x5 + 6x3 + 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 |
$9$ |
x9 + 3x5 + 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 |
$9$ |
x9 + 3x5 + 6x3 + 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 |
$9$ |
x9 + 3x5 + 3x3 + 3 |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 5/3]$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
$[5, 3, 0]$ |
$[1, 1]$ |