Learn more

Refine search


Results (1-50 of 795 matches)

Next   displayed columns for results
Label Polynomial $p$ $f$ $e$ $c$ Galois group $u$ $t$ Visible Artin slopes Visible Swan slopes Artin slope content Swan slope content Hidden Artin slopes Hidden Swan slopes Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia Resid. Poly Jump Set
3.9.1.0a1.1 $x^{9} + 2 x^{3} + 2 x^{2} + x + 1$ $3$ $9$ $1$ $0$ $C_9$ (as 9T1) $9$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{9}$ $[\ ]^{9}$ $[\ ]$ $[\ ]$ $t^{9} + 2 t^{3} + 2 t^{2} + t + 1$ $x - 3$ $[0]$ $[\ ]$ undefined
3.3.3.9a1.1 $( x^{3} + 2 x + 1 )^{3} + 6 ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $S_3\times C_3$ (as 9T4) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}]_{2}^{3}$ $[\frac{1}{2}]_{2}^{3}$ $[\ ]_{2}$ $[\ ]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 6 x + 3$ $[1, 0]$ $[1]$ $z + 2$ undefined
3.3.3.9a2.1 $( x^{3} + 2 x + 1 )^{3} + 3 ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $S_3\times C_3$ (as 9T4) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}]_{2}^{3}$ $[\frac{1}{2}]_{2}^{3}$ $[\ ]_{2}$ $[\ ]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 3 x + 3$ $[1, 0]$ $[1]$ $z + 1$ undefined
3.3.3.9a3.1 $( x^{3} + 2 x + 1 )^{3} + 6 x ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 6 t x + 3$ $[1, 0]$ $[1]$ $z + 2 t$ undefined
3.3.3.9a4.1 $( x^{3} + 2 x + 1 )^{3} + 3 x ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + t$ undefined
3.3.3.9a5.1 $( x^{3} + 2 x + 1 )^{3} + 6 x^{2} ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + 2 t^{2}$ undefined
3.3.3.9a6.1 $( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{2} + t)$ undefined
3.3.3.9a7.1 $( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 3\right) ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $C_3^2 : S_3 $ (as 9T13) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\frac{3}{2}]_{2}$ $[\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6\right) x + 3$ $[1, 0]$ $[1]$ $z + (2 t^{2} + t + 1)$ undefined
3.3.3.9a8.1 $( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 3\right) ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $C_3^2 : S_3 $ (as 9T13) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\frac{3}{2}]_{2}$ $[\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{2} + 1)$ undefined
3.3.3.9a9.1 $( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x\right) ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3 t\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{2} + 2 t)$ undefined
3.3.3.9a10.1 $( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 3\right) ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $9$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{3}{2}]$ $[\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 6 t + 3\right) x + 3$ $[1, 0]$ $[1]$ $z + (t^{2} + 2 t + 1)$ undefined
3.3.3.12a1.1 $( x^{3} + 2 x + 1 )^{3} + 3 ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $S_3\times C_3$ (as 9T4) $6$ $1$ $[2]$ $[1]$ $[2]^{6}$ $[1]^{6}$ $[\ ]^{2}$ $[\ ]^{2}$ $t^{3} + 2 t + 1$ $x^{3} + 3 x^{2} + 3$ $[2, 0]$ $[2]$ $z^{2} + 1$ undefined
3.3.3.12a2.1 $( x^{3} + 2 x + 1 )^{3} + 6 ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $C_3^2$ (as 9T2) $3$ $1$ $[2]$ $[1]$ $[2]^{3}$ $[1]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + 2 t + 1$ $x^{3} + 6 x^{2} + 3$ $[2, 0]$ $[1]$ $z^{2} + 2$ undefined
3.3.3.12a2.2 $( x^{3} + 2 x + 1 )^{3} + 6 ( x^{3} + 2 x + 1 )^{2} + 9 x^{2} + 3$ $3$ $3$ $3$ $12$ $C_9$ (as 9T1) $3$ $1$ $[2]$ $[1]$ $[2]^{3}$ $[1]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + 2 t + 1$ $x^{3} + 6 x^{2} + 9 t^{2} + 3$ $[2, 0]$ $[1]$ $z^{2} + 2$ undefined
3.3.3.12a2.3 $( x^{3} + 2 x + 1 )^{3} + 6 ( x^{3} + 2 x + 1 )^{2} + 18 x^{2} + 3$ $3$ $3$ $3$ $12$ $C_9$ (as 9T1) $3$ $1$ $[2]$ $[1]$ $[2]^{3}$ $[1]^{3}$ $[\ ]$ $[\ ]$ $t^{3} + 2 t + 1$ $x^{3} + 6 x^{2} + 18 t^{2} + 3$ $[2, 0]$ $[1]$ $z^{2} + 2$ undefined
3.3.3.12a3.1 $( x^{3} + 2 x + 1 )^{3} + 3 x ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $3$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{3}$ $[1,1,1]^{3}$ $[2,2]$ $[1,1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t + 3\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^{2} + t$ undefined
3.3.3.12a3.2 $( x^{3} + 2 x + 1 )^{3} + 3 x ( x^{3} + 2 x + 1 )^{2} + 12$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $3$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{3}$ $[1,1,1]^{3}$ $[2,2]$ $[1,1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t + 3\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^{2} + t$ undefined
3.3.3.12a3.3 $( x^{3} + 2 x + 1 )^{3} + 3 x ( x^{3} + 2 x + 1 )^{2} + 21$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $3$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{3}$ $[1,1,1]^{3}$ $[2,2]$ $[1,1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t + 3\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^{2} + t$ undefined
3.3.3.12a4.1 $( x^{3} + 2 x + 1 )^{3} + 6 x ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $(C_3^3:C_3):C_2$ (as 9T22) $6$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{6}$ $[1,1,1]^{6}$ $[2,2]^{2}$ $[1,1]^{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t + 6\right) x^{2} + 3$ $[2, 0]$ $[2]$ $z^{2} + 2 t$ undefined
3.3.3.12a5.1 $( x^{3} + 2 x + 1 )^{3} + 3 x^{2} ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $(C_3^3:C_3):C_2$ (as 9T22) $6$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{6}$ $[1,1,1]^{6}$ $[2,2]^{2}$ $[1,1]^{2}$ $t^{3} + 2 t + 1$ $x^{3} + 3 t^{2} x^{2} + 3$ $[2, 0]$ $[2]$ $z^{2} + t^{2}$ undefined
3.3.3.12a6.1 $( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x\right) ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $(C_3^3:C_3):C_2$ (as 9T22) $6$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{6}$ $[1,1,1]^{6}$ $[2,2]^{2}$ $[1,1]^{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3 t\right) x^{2} + 3$ $[2, 0]$ $[2]$ $z^{2} + (t^{2} + 2 t)$ undefined
3.3.3.12a7.1 $( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $C_9:C_3$ (as 9T6) $3$ $1$ $[2]$ $[1]$ $[2, 2]^{3}$ $[1,1]^{3}$ $[2]$ $[1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 6 t + 6\right) x^{2} + 18 t + 3$ $[2, 0]$ $[1]$ $z^{2} + (t^{2} + 2 t + 2)$ undefined
3.3.3.12a7.2 $( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 9 x + 3$ $3$ $3$ $3$ $12$ $C_3^2:C_3$ (as 9T7) $3$ $1$ $[2]$ $[1]$ $[2, 2]^{3}$ $[1,1]^{3}$ $[2]$ $[1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^{2} + (t^{2} + 2 t + 2)$ undefined
3.3.3.12a7.3 $( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 18 x + 3$ $3$ $3$ $3$ $12$ $C_9:C_3$ (as 9T6) $3$ $1$ $[2]$ $[1]$ $[2, 2]^{3}$ $[1,1]^{3}$ $[2]$ $[1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(3 t^{2} + 3\right) x^{2} + 9 t + 3$ $[2, 0]$ $[1]$ $z^{2} + (t^{2} + 2 t + 2)$ undefined
3.3.3.12a8.1 $( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $C_3^2 : S_3 $ (as 9T13) $6$ $1$ $[2]$ $[1]$ $[2, 2]^{6}$ $[1,1]^{6}$ $[2]^{2}$ $[1]^{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6\right) x^{2} + 3$ $[2, 0]$ $[2]$ $z^{2} + (2 t^{2} + 2)$ undefined
3.3.3.12a9.1 $( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $3$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{3}$ $[1,1,1]^{3}$ $[2,2]$ $[1,1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^{2} + (2 t^{2} + t)$ undefined
3.3.3.12a9.2 $( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 )^{2} + 12$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $3$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{3}$ $[1,1,1]^{3}$ $[2,2]$ $[1,1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^{2} + (2 t^{2} + t)$ undefined
3.3.3.12a9.3 $( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 )^{2} + 21$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $3$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{3}$ $[1,1,1]^{3}$ $[2,2]$ $[1,1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^{2} + (2 t^{2} + t)$ undefined
3.3.3.12a10.1 $( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $3$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{3}$ $[1,1,1]^{3}$ $[2,2]$ $[1,1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + 12$ $[2, 0]$ $[1]$ $z^{2} + (2 t^{2} + t + 2)$ undefined
3.3.3.12a10.2 $( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 12$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $3$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{3}$ $[1,1,1]^{3}$ $[2,2]$ $[1,1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 21$ $[2, 0]$ $[1]$ $z^{2} + (2 t^{2} + t + 2)$ undefined
3.3.3.12a10.3 $( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 21$ $3$ $3$ $3$ $12$ $C_3 \wr C_3 $ (as 9T17) $3$ $1$ $[2]$ $[1]$ $[2, 2, 2]^{3}$ $[1,1,1]^{3}$ $[2,2]$ $[1,1]$ $t^{3} + 2 t + 1$ $x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 3$ $[2, 0]$ $[1]$ $z^{2} + (2 t^{2} + t + 2)$ undefined
3.3.3.15a1.1 $( x^{3} + 2 x + 1 )^{3} + 3$ $3$ $3$ $3$ $15$ $S_3\times C_3$ (as 9T4) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{5}{2}]_{2}^{3}$ $[\frac{3}{2}]_{2}^{3}$ $[\ ]_{2}$ $[\ ]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.2 $( x^{3} + 2 x + 1 )^{3} + 9 x^{2} ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 9 t^{2} x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.3 $( x^{3} + 2 x + 1 )^{3} + 18 x^{2} ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 18 t^{2} x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.4 $( x^{3} + 2 x + 1 )^{3} + 9 x ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $C_3^2 : S_3 $ (as 9T13) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2}]_{2}$ $[\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(9 t + 9\right) x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.5 $( x^{3} + 2 x + 1 )^{3} + 18 x ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $C_3^2 : S_3 $ (as 9T13) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2}]_{2}$ $[\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(18 t + 18\right) x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.6 $( x^{3} + 2 x + 1 )^{3} + 9 ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $S_3\times C_3$ (as 9T4) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{5}{2}]_{2}^{3}$ $[\frac{3}{2}]_{2}^{3}$ $[\ ]_{2}$ $[\ ]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 9 x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.7 $( x^{3} + 2 x + 1 )^{3} + \left(9 x^{2} + 9\right) ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(9 t^{2} + 9 t + 18\right) x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.8 $( x^{3} + 2 x + 1 )^{3} + \left(18 x^{2} + 9\right) ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(18 t^{2} + 18 t\right) x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.9 $( x^{3} + 2 x + 1 )^{3} + 18 ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $S_3\times C_3$ (as 9T4) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{5}{2}]_{2}^{3}$ $[\frac{3}{2}]_{2}^{3}$ $[\ ]_{2}$ $[\ ]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 18 x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.10 $( x^{3} + 2 x + 1 )^{3} + \left(9 x^{2} + 18\right) ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(9 t^{2} + 18 t\right) x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.3.3.15a1.11 $( x^{3} + 2 x + 1 )^{3} + \left(18 x^{2} + 18\right) ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(18 t^{2} + 18 t + 9\right) x + 3$ $[3, 0]$ $[1]$ $z + 1$ undefined
3.1.9.9a1.1 $x^{9} + 3 x + 3$ $3$ $1$ $9$ $9$ $(C_3^2:C_8):C_2$ (as 9T19) $2$ $8$ $[\frac{9}{8}, \frac{9}{8}]$ $[\frac{1}{8},\frac{1}{8}]$ $[\frac{9}{8}, \frac{9}{8}]_{8}^{2}$ $[\frac{1}{8},\frac{1}{8}]_{8}^{2}$ $[\ ]^{2}_{8}$ $[\ ]^{2}_{8}$ $t + 1$ $x^{9} + 3 x + 3$ $[1, 1, 0]$ $[1]$ $z + 2$ undefined
3.1.9.9a1.2 $x^{9} + 6 x + 3$ $3$ $1$ $9$ $9$ $(C_3^2:C_8):C_2$ (as 9T19) $2$ $8$ $[\frac{9}{8}, \frac{9}{8}]$ $[\frac{1}{8},\frac{1}{8}]$ $[\frac{9}{8}, \frac{9}{8}]_{8}^{2}$ $[\frac{1}{8},\frac{1}{8}]_{8}^{2}$ $[\ ]^{2}_{8}$ $[\ ]^{2}_{8}$ $t + 1$ $x^{9} + 6 x + 3$ $[1, 1, 0]$ $[1]$ $z + 1$ undefined
3.1.9.10a1.1 $x^{9} + 3 x^{2} + 3$ $3$ $1$ $9$ $10$ $C_3^2:Q_8$ (as 9T14) $2$ $4$ $[\frac{5}{4}, \frac{5}{4}]$ $[\frac{1}{4},\frac{1}{4}]$ $[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ $[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ $[\ ]^{2}_{4}$ $[\ ]^{2}_{4}$ $t + 1$ $x^{9} + 3 x^{2} + 3$ $[2, 2, 0]$ $[2]$ $z^{2} + 1$ undefined
3.1.9.10a2.1 $x^{9} + 6 x^{2} + 3$ $3$ $1$ $9$ $10$ $S_3^2:C_2$ (as 9T16) $2$ $4$ $[\frac{5}{4}, \frac{5}{4}]$ $[\frac{1}{4},\frac{1}{4}]$ $[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ $[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ $[\ ]^{2}_{4}$ $[\ ]^{2}_{4}$ $t + 1$ $x^{9} + 6 x^{2} + 3$ $[2, 2, 0]$ $[1]$ $z^{2} + 2$ undefined
3.1.9.12a1.1 $x^{9} + 6 x^{4} + 3$ $3$ $1$ $9$ $12$ $C_3^2:C_4$ (as 9T9) $2$ $2$ $[\frac{3}{2}, \frac{3}{2}]$ $[\frac{1}{2},\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ $[\ ]^{2}_{2}$ $[\ ]^{2}_{2}$ $t + 1$ $x^{9} + 6 x^{4} + 3$ $[4, 4, 0]$ $[2]$ $z^{4} + 1$ undefined
3.1.9.12a2.1 $x^{9} + 3 x^{4} + 3$ $3$ $1$ $9$ $12$ $S_3^2$ (as 9T8) $2$ $2$ $[\frac{3}{2}, \frac{3}{2}]$ $[\frac{1}{2},\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ $[\ ]^{2}_{2}$ $[\ ]^{2}_{2}$ $t + 1$ $x^{9} + 3 x^{4} + 3$ $[4, 4, 0]$ $[2]$ $z^{4} + 2$ undefined
3.1.9.12a3.1 $x^{9} + 6 x^{4} + 3 x^{3} + 3$ $3$ $1$ $9$ $12$ $C_3^2 : C_6$ (as 9T11) $3$ $2$ $[\frac{3}{2}, \frac{3}{2}]$ $[\frac{1}{2},\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\ ]^{3}_{2}$ $[\ ]^{3}_{2}$ $t + 1$ $x^{9} + 6 x^{4} + 3 x^{3} + 3$ $[4, 3, 0]$ $[3]$ $z^{4} + 2 z + 1$ undefined
3.1.9.12a3.2 $x^{9} + 6 x^{4} + 6 x^{3} + 3$ $3$ $1$ $9$ $12$ $C_3^2 : C_6$ (as 9T11) $3$ $2$ $[\frac{3}{2}, \frac{3}{2}]$ $[\frac{1}{2},\frac{1}{2}]$ $[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ $[\ ]^{3}_{2}$ $[\ ]^{3}_{2}$ $t + 1$ $x^{9} + 6 x^{4} + 6 x^{3} + 3$ $[4, 3, 0]$ $[3]$ $z^{4} + z + 1$ undefined
Next   displayed columns for results