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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group Num. automorphisms
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Results (6 matches)

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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
3.3.3.15a1.2 $( x^{3} + 2 x + 1 )^{3} + 9 x^{2} ( x^{3} + 2 x + 1 ) + 3$ $3$ $3$ $3$ $15$ $(C_3^3:C_3):C_2$ (as 9T22) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 9 t^{2} x + 3$ $[3, 0]$ $[1]$ $z + 2$ 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) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + 18 t^{2} x + 3$ $[3, 0]$ $[1]$ $z + 2$ 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) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(9 t^{2} + 9 t + 18\right) x + 3$ $[3, 0]$ $[1]$ $z + 2$ 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) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(18 t^{2} + 18 t\right) x + 3$ $[3, 0]$ $[1]$ $z + 2$ 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) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(9 t^{2} + 18 t\right) x + 3$ $[3, 0]$ $[1]$ $z + 2$ 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) $3$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ $[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ $[\frac{3}{2},\frac{3}{2}]_{2}$ $[\frac{1}{2},\frac{1}{2}]_{2}$ $t^{3} + 2 t + 1$ $x^{3} + \left(18 t^{2} + 18 t + 9\right) x + 3$ $[3, 0]$ $[1]$ $z + 2$ undefined
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