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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content
3.9.0.1 x9 + 2x3 + 2x2 + x + 1 $3$ $1$ $9$ $0$ $C_9$ (as 9T1) $[\ ]$ $[\ ]^{9}$
3.9.9.1 x9 + 90x7 - 207x6 + 540x5 + 324x4 + 243x3 + 324x2 + 162x + 27 $3$ $3$ $3$ $9$ $S_3\times C_3$ (as 9T4) $[3/2]$ $[3/2]_{2}^{3}$
3.9.9.10 x9 - 24x8 + 321x7 - 117x6 - 243x5 + 1062x4 + 1053x3 + 135x2 - 27x + 27 $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $[3/2]$ $[3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.11 x9 + 3x + 3 $3$ $9$ $1$ $9$ $(C_3^2:C_8):C_2$ (as 9T19) $[9/8, 9/8]$ $[9/8, 9/8]_{8}^{2}$
3.9.9.12 x9 + 6x + 3 $3$ $9$ $1$ $9$ $(C_3^2:C_8):C_2$ (as 9T19) $[9/8, 9/8]$ $[9/8, 9/8]_{8}^{2}$
3.9.9.2 x9 - 3x7 + 9x6 - 9x5 - 18x4 + 81x3 - 27x2 - 27x + 27 $3$ $3$ $3$ $9$ $C_3^2 : S_3 $ (as 9T13) $[3/2]$ $[3/2, 3/2]_{2}^{3}$
3.9.9.3 x9 - 3x8 + 126x7 + 198x6 + 297x5 + 567x4 + 324x3 + 108x2 + 81x + 27 $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $[3/2]$ $[3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.4 x9 - 24x8 + 318x7 - 189x6 + 1080x5 + 2826x4 + 1350x3 - 108x2 - 54x + 27 $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $[3/2]$ $[3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.5 x9 - 24x7 + 9x6 + 216x5 - 144x4 + 648x2 - 216x + 27 $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $[3/2]$ $[3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.6 x9 - 6x8 + 45x7 + 594x6 + 99x5 + 108x4 - 54x3 + 27x2 + 81x + 27 $3$ $3$ $3$ $9$ $S_3\times C_3$ (as 9T4) $[3/2]$ $[3/2]_{2}^{3}$
3.9.9.7 x9 - 6x7 + 9x6 - 36x5 - 36x4 + 459x3 - 108x2 - 54x + 27 $3$ $3$ $3$ $9$ $C_3^2 : S_3 $ (as 9T13) $[3/2]$ $[3/2, 3/2]_{2}^{3}$
3.9.9.8 x9 + 6x8 + 114x7 + 549x6 + 522x5 + 495x4 + 216x3 + 297x2 - 108x + 27 $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $[3/2]$ $[3/2, 3/2, 3/2]_{2}^{3}$
3.9.9.9 x9 + 9x6 + 72x5 - 189x3 + 216x2 + 27 $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $[3/2]$ $[3/2, 3/2, 3/2]_{2}^{3}$
3.9.10.1 x9 + 3x2 + 3 $3$ $9$ $1$ $10$ $C_3^2:Q_8$ (as 9T14) $[5/4, 5/4]$ $[5/4, 5/4]_{4}^{2}$
3.9.10.2 x9 + 6x2 + 3 $3$ $9$ $1$ $10$ $S_3^2:C_2$ (as 9T16) $[5/4, 5/4]$ $[5/4, 5/4]_{4}^{2}$
3.9.12.1 x9 + 18x8 + 108x7 + 225x6 + 108x5 + 324x4 + 675x3 + 4050x2 - 3861 $3$ $3$ $3$ $12$ $C_3^2$ (as 9T2) $[2]$ $[2]^{3}$
3.9.12.10 x9 + 9x8 + 45x7 + 90x6 + 324x5 + 621x4 + 594x3 + 2349x2 + 2943 $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$
3.9.12.11 x9 - 24x8 + 324x7 - 459x6 + 828x5 - 972x4 + 540x3 - 216x2 + 432 $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$
3.9.12.12 x9 + 9x8 + 45x7 + 54x6 + 189x5 + 540x4 + 297x3 + 1944x2 + 3834 $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$
3.9.12.13 x9 - 6x8 + 144x7 + 927x6 + 504x5 + 4320x4 + 1971x3 + 11286x2 + 17037 $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$
3.9.12.14 x9 - 6x8 + 144x7 + 900x6 + 612x5 + 3024x4 + 1080x3 + 6264x2 + 3672 $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$
3.9.12.15 x9 - 24x8 + 216x7 - 27x6 + 477x5 + 1134x4 + 1026x3 + 3348x2 + 6021 $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$
3.9.12.16 x9 + 9x8 + 27x7 + 36x6 + 54x5 + 81x4 + 675x3 + 2025x2 - 3861 $3$ $3$ $3$ $12$ $S_3\times C_3$ (as 9T4) $[2]$ $[2]^{6}$
3.9.12.17 x9 - 6x8 - 36x7 + 441x6 + 126x5 + 216x4 + 189x3 + 1404x2 - 216 $3$ $3$ $3$ $12$ $C_3^2 : S_3 $ (as 9T13) $[2]$ $[2, 2]^{6}$
3.9.12.18 x9 - 12x8 + 36x7 + 90x6 - 342x5 + 432x4 + 1971x3 - 1890x2 + 17037 $3$ $3$ $3$ $12$ $(C_3^3:C_3):C_2$ (as 9T22) $[2]$ $[2, 2, 2]^{6}$
3.9.12.19 x9 + 18x8 + 180x7 + 495x6 + 1188x5 + 4428x4 + 1971x3 + 15066x2 + 17037 $3$ $3$ $3$ $12$ $(C_3^3:C_3):C_2$ (as 9T22) $[2]$ $[2, 2, 2]^{6}$
3.9.12.2 x9 + 18x8 + 108x7 + 243x6 + 324x5 + 972x4 + 1269x3 + 7614x2 + 15984 $3$ $3$ $3$ $12$ $C_9$ (as 9T1) $[2]$ $[2]^{3}$
3.9.12.20 x9 - 12x8 + 81x7 - 45x6 + 117x5 - 162x4 + 189x3 - 270x2 - 216 $3$ $3$ $3$ $12$ $(C_3^3:C_3):C_2$ (as 9T22) $[2]$ $[2, 2, 2]^{6}$
3.9.12.21 x9 + 6x4 + 3 $3$ $9$ $1$ $12$ $C_3^2:C_4$ (as 9T9) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{2}$
3.9.12.22 x9 + 6x4 + 6x3 + 3 $3$ $9$ $1$ $12$ $C_3^2 : C_6$ (as 9T11) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{3}$
3.9.12.23 x9 + 6x4 + 3x3 + 3 $3$ $9$ $1$ $12$ $C_3^2 : C_6$ (as 9T11) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{3}$
3.9.12.24 x9 + 3x4 + 3 $3$ $9$ $1$ $12$ $S_3^2$ (as 9T8) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{2}$
3.9.12.25 x9 + 3x4 + 6x3 + 3 $3$ $9$ $1$ $12$ $C_3^2:C_8$ (as 9T15) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{4}$
3.9.12.26 x9 + 3x4 + 3x3 + 3 $3$ $9$ $1$ $12$ $C_3^2:C_8$ (as 9T15) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{4}$
3.9.12.3 x9 + 18x8 + 108x7 + 153x6 - 756x5 - 2268x4 + 891x3 + 5346x2 + 9099 $3$ $3$ $3$ $12$ $C_9$ (as 9T1) $[2]$ $[2]^{3}$
3.9.12.4 x9 + 6x8 + 45x7 + 252x6 + 144x5 + 540x4 + 432x3 + 864x2 + 1728 $3$ $3$ $3$ $12$ $C_3^2:C_3$ (as 9T7) $[2]$ $[2, 2]^{3}$
3.9.12.5 x9 + 6x8 + 126x7 + 468x6 + 630x5 + 1674x4 + 675x3 - 108x2 - 3861 $3$ $3$ $3$ $12$ $C_9:C_3$ (as 9T6) $[2]$ $[2, 2]^{3}$
3.9.12.6 x9 - 3x8 - 9x7 + 63x6 + 63x5 + 54x4 + 189x3 + 702x2 - 216 $3$ $3$ $3$ $12$ $C_9:C_3$ (as 9T6) $[2]$ $[2, 2]^{3}$
3.9.12.7 x9 - 6x8 + 36x7 + 621x6 + 477x5 + 3996x4 + 1026x3 + 9504x2 + 6021 $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$
3.9.12.8 x9 - 24x8 + 324x7 - 405x6 - 36x5 + 4860x4 + 540x3 + 6912x2 + 7236 $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$
3.9.12.9 x9 + 9x8 + 45x7 + 117x6 + 486x5 + 1026x4 + 1485x3 + 5994x2 + 11934 $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$
3.9.13.1 x9 + 6x5 + 3 $3$ $9$ $1$ $13$ $(C_3^2:C_8):C_2$ (as 9T19) $[13/8, 13/8]$ $[13/8, 13/8]_{8}^{2}$
3.9.13.10 x9 + 6x6 + 3x5 + 3x3 + 3 $3$ $9$ $1$ $13$ $C_3 \wr S_3 $ (as 9T20) $[3/2, 5/3]$ $[3/2, 3/2, 5/3]_{2}^{3}$
3.9.13.2 x9 + 6x5 + 3x3 + 3 $3$ $9$ $1$ $13$ $C_3^2 : D_{6} $ (as 9T18) $[3/2, 5/3]$ $[3/2, 3/2, 5/3]_{2}^{2}$
3.9.13.3 x9 + 3x6 + 6x5 + 6x3 + 3 $3$ $9$ $1$ $13$ $C_3 \wr S_3 $ (as 9T20) $[3/2, 5/3]$ $[3/2, 3/2, 5/3]_{2}^{3}$
3.9.13.4 x9 + 6x5 + 6x3 + 3 $3$ $9$ $1$ $13$ $C_3 \wr S_3 $ (as 9T20) $[3/2, 5/3]$ $[3/2, 3/2, 5/3]_{2}^{3}$
3.9.13.5 x9 + 6x6 + 6x5 + 6x3 + 3 $3$ $9$ $1$ $13$ $C_3 \wr S_3 $ (as 9T20) $[3/2, 5/3]$ $[3/2, 3/2, 5/3]_{2}^{3}$
3.9.13.6 x9 + 3x5 + 3 $3$ $9$ $1$ $13$ $(C_3^2:C_8):C_2$ (as 9T19) $[13/8, 13/8]$ $[13/8, 13/8]_{8}^{2}$
3.9.13.7 x9 + 3x5 + 6x3 + 3 $3$ $9$ $1$ $13$ $C_3^2 : D_{6} $ (as 9T18) $[3/2, 5/3]$ $[3/2, 3/2, 5/3]_{2}^{2}$
3.9.13.8 x9 + 3x5 + 3x3 + 3 $3$ $9$ $1$ $13$ $C_3 \wr S_3 $ (as 9T20) $[3/2, 5/3]$ $[3/2, 3/2, 5/3]_{2}^{3}$
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