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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
3.2.6.22a1.13 $( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + \left(18 t + 18\right) x^{2} + \left(9 t + 18\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.14 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + \left(18 t + 18\right) x^{2} + \left(9 t + 18\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.15 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + \left(9 t + 9\right) x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.16 $( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + \left(18 t + 9\right) x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.17 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 9 x^{3} + \left(18 t + 9\right) x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.18 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 9 x^{3} + 9 t x^{2} + \left(9 t + 18\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.22 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + \left(9 t + 18\right) x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.23 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 9 ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 9 x^{3} + \left(9 t + 18\right) x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.24 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 9 ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + \left(9 t + 18\right) x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.25 $( x^{2} + 2 x + 2 )^{6} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + \left(9 t + 9\right) x^{2} + \left(9 t + 18\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.26 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 9 x^{3} + \left(18 t + 18\right) x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.27 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + \left(18 t + 18\right) x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.31 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 9 t x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.32 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + \left(18 t + 9\right) x^{2} + \left(9 t + 18\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.33 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + 9 t x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.34 $( x^{2} + 2 x + 2 )^{6} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + \left(9 t + 18\right) x^{2} + \left(9 t + 18\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.35 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 9 x^{3} + 18 t x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.36 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $2$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, 2, \frac{5}{2}]_{2}^{2}$ $[\frac{1}{2},1,1,\frac{3}{2}]_{2}^{2}$ $[\frac{3}{2},2,2]$ $[\frac{1}{2},1,1]$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + 18 t x^{2} + 9 t x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.59 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $6$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{6}$ $[\frac{1}{2},1,\frac{3}{2}]_{2}^{6}$ $[\frac{3}{2},2]^{3}$ $[\frac{1}{2},1]^{3}$ $t^{2} + 2 t + 2$ $x^{6} + 9 x^{3} + \left(9 t + 9\right) x^{2} + \left(9 t + 9\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.60 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $6$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{6}$ $[\frac{1}{2},1,\frac{3}{2}]_{2}^{6}$ $[\frac{3}{2},2]^{3}$ $[\frac{1}{2},1]^{3}$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + \left(9 t + 9\right) x^{2} + \left(9 t + 9\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.64 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 9 ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $6$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{6}$ $[\frac{1}{2},1,\frac{3}{2}]_{2}^{6}$ $[\frac{3}{2},2]^{3}$ $[\frac{1}{2},1]^{3}$ $t^{2} + 2 t + 2$ $x^{6} + 9 x^{3} + \left(9 t + 18\right) x^{2} + \left(9 t + 9\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.65 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 9 ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $6$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{6}$ $[\frac{1}{2},1,\frac{3}{2}]_{2}^{6}$ $[\frac{3}{2},2]^{3}$ $[\frac{1}{2},1]^{3}$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + \left(9 t + 18\right) x^{2} + \left(9 t + 9\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.69 $( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $6$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{6}$ $[\frac{1}{2},1,\frac{3}{2}]_{2}^{6}$ $[\frac{3}{2},2]^{3}$ $[\frac{1}{2},1]^{3}$ $t^{2} + 2 t + 2$ $x^{6} + 18 x^{3} + \left(18 t + 9\right) x^{2} + \left(9 t + 9\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
3.2.6.22a1.70 $( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ $3$ $2$ $6$ $22$ $C_3\wr C_2^2$ (as 12T130) $6$ $2$ $[\frac{5}{2}]$ $[\frac{3}{2}]$ $[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{6}$ $[\frac{1}{2},1,\frac{3}{2}]_{2}^{6}$ $[\frac{3}{2},2]^{3}$ $[\frac{1}{2},1]^{3}$ $t^{2} + 2 t + 2$ $x^{6} + 9 x^{3} + \left(18 t + 9\right) x^{2} + \left(9 t + 9\right) x + 3$ $[6, 0]$ $[1, 1]$ $z^3 + 2,2 z^2 + 2$ $[1, 7]$
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