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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
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Results (26 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
3.9.12.1 $x^{9} + 18 x^{8} + 108 x^{7} + 225 x^{6} + 108 x^{5} + 324 x^{4} + 675 x^{3} + 4050 x^{2} - 3861$ $3$ $3$ $3$ $12$ $C_3^2$ (as 9T2) $[2]$ $[2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + 6 x^{2} + 18 t + 3$
3.9.12.10 $x^{9} + 9 x^{8} + 45 x^{7} + 90 x^{6} + 324 x^{5} + 621 x^{4} + 594 x^{3} + 2349 x^{2} + 2943$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t + 3\right) x^{2} + 9 t + 12$
3.9.12.11 $x^{9} - 24 x^{8} + 324 x^{7} - 459 x^{6} + 828 x^{5} - 972 x^{4} + 540 x^{3} - 216 x^{2} + 432$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 9 t^{2} + 9 t + 3$
3.9.12.12 $x^{9} + 9 x^{8} + 45 x^{7} + 54 x^{6} + 189 x^{5} + 540 x^{4} + 297 x^{3} + 1944 x^{2} + 3834$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t + 3\right) x^{2} + 9 t^{2} + 9 t + 12$
3.9.12.13 $x^{9} - 6 x^{8} + 144 x^{7} + 927 x^{6} + 504 x^{5} + 4320 x^{4} + 1971 x^{3} + 11286 x^{2} + 17037$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 18 t + 21$
3.9.12.14 $x^{9} - 6 x^{8} + 144 x^{7} + 900 x^{6} + 612 x^{5} + 3024 x^{4} + 1080 x^{3} + 6264 x^{2} + 3672$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 18 t + 12$
3.9.12.15 $x^{9} - 24 x^{8} + 216 x^{7} - 27 x^{6} + 477 x^{5} + 1134 x^{4} + 1026 x^{3} + 3348 x^{2} + 6021$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t\right) x^{2} + 9 t^{2} + 18 t + 12$
3.9.12.16 $x^{9} + 9 x^{8} + 27 x^{7} + 36 x^{6} + 54 x^{5} + 81 x^{4} + 675 x^{3} + 2025 x^{2} - 3861$ $3$ $3$ $3$ $12$ $S_3\times C_3$ (as 9T4) $[2]$ $[2]^{6}$ $t^{3} + 2 t + 1$ $x^{3} + 3 x^{2} + 18 t + 3$
3.9.12.17 $x^{9} - 6 x^{8} - 36 x^{7} + 441 x^{6} + 126 x^{5} + 216 x^{4} + 189 x^{3} + 1404 x^{2} - 216$ $3$ $3$ $3$ $12$ $C_3^2 : S_3 $ (as 9T13) $[2]$ $[2, 2]^{6}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6\right) x^{2} + 9 t + 3$
3.9.12.18 $x^{9} - 12 x^{8} + 36 x^{7} + 90 x^{6} - 342 x^{5} + 432 x^{4} + 1971 x^{3} - 1890 x^{2} + 17037$ $3$ $3$ $3$ $12$ $(C_3^3:C_3):C_2$ (as 9T22) $[2]$ $[2, 2, 2]^{6}$ $t^{3} + 2 t + 1$ $x^{3} + 3 t^{2} x^{2} + 18 t + 21$
3.9.12.19 $x^{9} + 18 x^{8} + 180 x^{7} + 495 x^{6} + 1188 x^{5} + 4428 x^{4} + 1971 x^{3} + 15066 x^{2} + 17037$ $3$ $3$ $3$ $12$ $(C_3^3:C_3):C_2$ (as 9T22) $[2]$ $[2, 2, 2]^{6}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t + 6\right) x^{2} + 18 t + 21$
3.9.12.2 $x^{9} + 18 x^{8} + 108 x^{7} + 243 x^{6} + 324 x^{5} + 972 x^{4} + 1269 x^{3} + 7614 x^{2} + 15984$ $3$ $3$ $3$ $12$ $C_9$ (as 9T1) $[2]$ $[2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + 6 x^{2} + 9 t^{2} + 18 t + 21$
3.9.12.20 $x^{9} - 12 x^{8} + 81 x^{7} - 45 x^{6} + 117 x^{5} - 162 x^{4} + 189 x^{3} - 270 x^{2} - 216$ $3$ $3$ $3$ $12$ $(C_3^3:C_3):C_2$ (as 9T22) $[2]$ $[2, 2, 2]^{6}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3 t\right) x^{2} + 9 t + 3$
3.9.12.21 $x^{9} + 6 x^{4} + 3$ $3$ $9$ $1$ $12$ $C_3^2:C_4$ (as 9T9) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{2}$ $t + 1$ $x^{9} + 6 x^{4} + 3$
3.9.12.22 $x^{9} + 6 x^{4} + 6 x^{3} + 3$ $3$ $9$ $1$ $12$ $C_3^2 : C_6$ (as 9T11) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{3}$ $t + 1$ $x^{9} + 6 x^{4} + 6 x^{3} + 3$
3.9.12.23 $x^{9} + 6 x^{4} + 3 x^{3} + 3$ $3$ $9$ $1$ $12$ $C_3^2 : C_6$ (as 9T11) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{3}$ $t + 1$ $x^{9} + 6 x^{4} + 3 x^{3} + 3$
3.9.12.24 $x^{9} + 3 x^{4} + 3$ $3$ $9$ $1$ $12$ $S_3^2$ (as 9T8) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{2}$ $t + 1$ $x^{9} + 3 x^{4} + 3$
3.9.12.25 $x^{9} + 3 x^{4} + 6 x^{3} + 3$ $3$ $9$ $1$ $12$ $C_3^2:C_8$ (as 9T15) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{4}$ $t + 1$ $x^{9} + 3 x^{4} + 6 x^{3} + 3$
3.9.12.26 $x^{9} + 3 x^{4} + 3 x^{3} + 3$ $3$ $9$ $1$ $12$ $C_3^2:C_8$ (as 9T15) $[3/2, 3/2]$ $[3/2, 3/2]_{2}^{4}$ $t + 1$ $x^{9} + 3 x^{4} + 3 x^{3} + 3$
3.9.12.3 $x^{9} + 18 x^{8} + 108 x^{7} + 153 x^{6} - 756 x^{5} - 2268 x^{4} + 891 x^{3} + 5346 x^{2} + 9099$ $3$ $3$ $3$ $12$ $C_9$ (as 9T1) $[2]$ $[2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + 6 x^{2} + 18 t^{2} + 3$
3.9.12.4 $x^{9} + 6 x^{8} + 45 x^{7} + 252 x^{6} + 144 x^{5} + 540 x^{4} + 432 x^{3} + 864 x^{2} + 1728$ $3$ $3$ $3$ $12$ $C_3^2:C_3$ (as 9T7) $[2]$ $[2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3 t + 6\right) x^{2} + 12$
3.9.12.5 $x^{9} + 6 x^{8} + 126 x^{7} + 468 x^{6} + 630 x^{5} + 1674 x^{4} + 675 x^{3} - 108 x^{2} - 3861$ $3$ $3$ $3$ $12$ $C_9:C_3$ (as 9T6) $[2]$ $[2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 6 t + 6\right) x^{2} + 18 t + 3$
3.9.12.6 $x^{9} - 3 x^{8} - 9 x^{7} + 63 x^{6} + 63 x^{5} + 54 x^{4} + 189 x^{3} + 702 x^{2} - 216$ $3$ $3$ $3$ $12$ $C_9:C_3$ (as 9T6) $[2]$ $[2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3\right) x^{2} + 9 t + 3$
3.9.12.7 $x^{9} - 6 x^{8} + 36 x^{7} + 621 x^{6} + 477 x^{5} + 3996 x^{4} + 1026 x^{3} + 9504 x^{2} + 6021$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + 9 t^{2} + 18 t + 12$
3.9.12.8 $x^{9} - 24 x^{8} + 324 x^{7} - 405 x^{6} - 36 x^{5} + 4860 x^{4} + 540 x^{3} + 6912 x^{2} + 7236$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 9 t^{2} + 9 t + 21$
3.9.12.9 $x^{9} + 9 x^{8} + 45 x^{7} + 117 x^{6} + 486 x^{5} + 1026 x^{4} + 1485 x^{3} + 5994 x^{2} + 11934$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $[2]$ $[2, 2, 2]^{3}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t + 3\right) x^{2} + 9 t + 21$
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