Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Slope content |
3.9.0.1 |
$9$ |
x9 - x3 + x2 + 1 |
$3$ |
$1$ |
$9$ |
$0$ |
$C_9$ (as 9T1) |
$9$ |
$1$ |
$[\ ]^{9}$ |
3.9.9.1 |
$9$ |
x9 + 54x5 + 27x3 + 189 |
$3$ |
$3$ |
$3$ |
$9$ |
$S_3\times C_3$ (as 9T4) |
$3$ |
$2$ |
$[3/2]_{2}^{3}$ |
3.9.9.10 |
$9$ |
x9 + 6x6 + 9x4 + 27 |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
3.9.9.11 |
$9$ |
x9 + 3x + 3 |
$3$ |
$9$ |
$1$ |
$9$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[9/8, 9/8]_{8}^{2}$ |
3.9.9.12 |
$9$ |
x9 + 6x + 6 |
$3$ |
$9$ |
$1$ |
$9$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[9/8, 9/8]_{8}^{2}$ |
3.9.9.2 |
$9$ |
x9 + 18x3 + 27x + 27 |
$3$ |
$3$ |
$3$ |
$9$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[3/2, 3/2]_{2}^{3}$ |
3.9.9.3 |
$9$ |
x9 + 9x4 + 18x3 + 54 |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
3.9.9.4 |
$9$ |
x9 + 3x6 + 9x4 + 54 |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
3.9.9.5 |
$9$ |
x9 + 3x7 + 3x6 + 54 |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
3.9.9.6 |
$9$ |
x9 + 3x7 + 3x6 + 18x4 + 54 |
$3$ |
$3$ |
$3$ |
$9$ |
$S_3\times C_3$ (as 9T4) |
$3$ |
$2$ |
$[3/2]_{2}^{3}$ |
3.9.9.7 |
$9$ |
x9 + 18x3 + 54x + 27 |
$3$ |
$3$ |
$3$ |
$9$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[3/2, 3/2]_{2}^{3}$ |
3.9.9.8 |
$9$ |
x9 + 6x7 + 18x3 + 27 |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
3.9.9.9 |
$9$ |
x9 + 18x5 + 27x2 + 54 |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[3/2, 3/2, 3/2]_{2}^{3}$ |
3.9.10.1 |
$9$ |
x9 + 3x2 + 3 |
$3$ |
$9$ |
$1$ |
$10$ |
$C_3^2:Q_8$ (as 9T14) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
3.9.10.2 |
$9$ |
x9 + 3x2 + 6 |
$3$ |
$9$ |
$1$ |
$10$ |
$S_3^2:C_2$ (as 9T16) |
$2$ |
$4$ |
$[5/4, 5/4]_{4}^{2}$ |
3.9.12.1 |
$9$ |
x9 + 18x5 + 18x3 + 27x2 + 216 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2$ (as 9T2) |
$3$ |
$1$ |
$[2]^{3}$ |
3.9.12.10 |
$9$ |
x9 + 24x6 + 18x5 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2, 2, 2]^{3}$ |
3.9.12.11 |
$9$ |
x9 + 21x6 + 54x2 + 54 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2, 2, 2]^{3}$ |
3.9.12.12 |
$9$ |
x9 + 3x6 + 18x5 + 54 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2, 2, 2]^{3}$ |
3.9.12.13 |
$9$ |
x9 + 3x8 + 72x3 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2, 2, 2]^{3}$ |
3.9.12.14 |
$9$ |
x9 + 3x8 + 45x3 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2, 2, 2]^{3}$ |
3.9.12.15 |
$9$ |
x9 + 72x3 + 54x2 + 54 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2, 2, 2]^{3}$ |
3.9.12.16 |
$9$ |
x9 + 9x5 + 18x3 + 27x2 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$S_3\times C_3$ (as 9T4) |
$6$ |
$1$ |
$[2]^{6}$ |
3.9.12.17 |
$9$ |
x9 + 6x8 + 6x6 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2 : S_3 $ (as 9T13) |
$6$ |
$1$ |
$[2, 2]^{6}$ |
3.9.12.18 |
$9$ |
x9 + 6x8 + 18x3 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$6$ |
$1$ |
$[2, 2, 2]^{6}$ |
3.9.12.19 |
$9$ |
x9 + 6x8 + 18x5 + 18x3 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$6$ |
$1$ |
$[2, 2, 2]^{6}$ |
3.9.12.2 |
$9$ |
x9 + 18x5 + 18x3 + 27x2 + 54 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]^{3}$ |
3.9.12.20 |
$9$ |
x9 + 6x6 + 54x2 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$6$ |
$1$ |
$[2, 2, 2]^{6}$ |
3.9.12.21 |
$9$ |
x9 + 3x4 + 6 |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2:C_4$ (as 9T9) |
$2$ |
$2$ |
$[3/2, 3/2]_{2}^{2}$ |
3.9.12.22 |
$9$ |
x9 + 6x4 + 6x3 + 3 |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2 : C_6$ (as 9T11) |
$3$ |
$2$ |
$[3/2, 3/2]_{2}^{3}$ |
3.9.12.23 |
$9$ |
x9 + 6x4 + 3x3 + 3 |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2 : C_6$ (as 9T11) |
$3$ |
$2$ |
$[3/2, 3/2]_{2}^{3}$ |
3.9.12.24 |
$9$ |
x9 + 3x4 + 3 |
$3$ |
$9$ |
$1$ |
$12$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[3/2, 3/2]_{2}^{2}$ |
3.9.12.25 |
$9$ |
x9 + 3x4 + 6x3 + 3 |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2:C_8$ (as 9T15) |
$4$ |
$2$ |
$[3/2, 3/2]_{2}^{4}$ |
3.9.12.26 |
$9$ |
x9 + 3x4 + 3x3 + 3 |
$3$ |
$9$ |
$1$ |
$12$ |
$C_3^2:C_8$ (as 9T15) |
$4$ |
$2$ |
$[3/2, 3/2]_{2}^{4}$ |
3.9.12.3 |
$9$ |
x9 + 6x8 + 3x6 + 9x3 + 135 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]^{3}$ |
3.9.12.4 |
$9$ |
x9 + 6x6 + 18x5 + 36x3 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2:C_3$ (as 9T7) |
$3$ |
$1$ |
$[2, 2]^{3}$ |
3.9.12.5 |
$9$ |
x9 + 18x5 + 18x3 + 27x2 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9:C_3$ (as 9T6) |
$3$ |
$1$ |
$[2, 2]^{3}$ |
3.9.12.6 |
$9$ |
x9 + 3x8 + 6x6 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9:C_3$ (as 9T6) |
$3$ |
$1$ |
$[2, 2]^{3}$ |
3.9.12.7 |
$9$ |
x9 + 18x5 + 72x3 + 54 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2, 2, 2]^{3}$ |
3.9.12.8 |
$9$ |
x9 + 12x6 + 54x2 + 54 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2, 2, 2]^{3}$ |
3.9.12.9 |
$9$ |
x9 + 15x6 + 18x5 + 27 |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2, 2, 2]^{3}$ |
3.9.13.1 |
$9$ |
x9 + 6x5 + 6 |
$3$ |
$9$ |
$1$ |
$13$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[13/8, 13/8]_{8}^{2}$ |
3.9.13.10 |
$9$ |
x9 + 3x6 + 3x5 + 3x3 + 6 |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
3.9.13.2 |
$9$ |
x9 + 6x5 + 3x3 + 3 |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[3/2, 3/2, 5/3]_{2}^{2}$ |
3.9.13.3 |
$9$ |
x9 + 3x6 + 6x5 + 6x3 + 3 |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
3.9.13.4 |
$9$ |
x9 + 6x5 + 6x3 + 3 |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
3.9.13.5 |
$9$ |
x9 + 6x6 + 6x5 + 6x3 + 3 |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |
3.9.13.6 |
$9$ |
x9 + 3x5 + 3 |
$3$ |
$9$ |
$1$ |
$13$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[13/8, 13/8]_{8}^{2}$ |
3.9.13.7 |
$9$ |
x9 + 3x5 + 6x3 + 3 |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3^2 : D_{6} $ (as 9T18) |
$2$ |
$2$ |
$[3/2, 3/2, 5/3]_{2}^{2}$ |
3.9.13.8 |
$9$ |
x9 + 3x5 + 3x3 + 6 |
$3$ |
$9$ |
$1$ |
$13$ |
$C_3 \wr S_3 $ (as 9T20) |
$3$ |
$2$ |
$[3/2, 3/2, 5/3]_{2}^{3}$ |