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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group Num. automorphisms
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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
2.2.6.20a1.41 $( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{3} + 2$ $2$ $2$ $6$ $20$ $C_2^3:S_4$ (as 12T106) $2$ $3$ $[\frac{8}{3}]$ $[\frac{5}{3}]$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{8}{3}]$ $[\frac{1}{3},\frac{1}{3},1,\frac{5}{3}]$ $t^{2} + t + 1$ $x^{6} + 2 x^{5} + 4 t x^{3} + 2$ $[5, 0]$ $[1, 1]$ $z^4 + z^2 + 1,z + 1$ $[3, 9]$
2.2.6.20a1.42 $( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 2$ $2$ $2$ $6$ $20$ $C_2^3.S_4$ (as 12T107) $2$ $3$ $[\frac{8}{3}]$ $[\frac{5}{3}]$ $[\frac{4}{3}, \frac{4}{3}, 2, \frac{8}{3}, \frac{8}{3}]_{3}^{2}$ $[\frac{1}{3},\frac{1}{3},1,\frac{5}{3},\frac{5}{3}]_{3}^{2}$ $[\frac{4}{3},\frac{4}{3},2,\frac{8}{3}]$ $[\frac{1}{3},\frac{1}{3},1,\frac{5}{3}]$ $t^{2} + t + 1$ $x^{6} + 2 x^{5} + 4 t x^{4} + \left(4 t + 4\right) x^{3} + 2$ $[5, 0]$ $[1, 1]$ $z^4 + z^2 + 1,z + 1$ $[3, 9]$
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