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Note: Search results may be incomplete due to uncomputed quantities: galois_label (239087 objects)

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Degree $n$ Residue characteristic $p$ Discriminant exponent $c$ Galois group
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$
Num. automorphisms Inertia subgroup Indices Assoc. Inertia Jump Set
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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Results (15 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
3.2.9.44a1.5 $( x^{2} + 2 x + 2 )^{9} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 3$ $3$ $2$ $9$ $44$ $C_3\times D_9$ (as 18T19) not computed not computed $[2, 3]$ $[1,2]$ not computed not computed not computed not computed $t^{2} + 2 t + 2$ $x^{9} + \left(9 t + 9\right) x^{8} + 3 x^{6} + 18 x^{5} + 54 t + 3$ $[14, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z^2 + 2$ undefined
3.2.9.44a1.9 $( x^{2} + 2 x + 2 )^{9} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{8} + 3 ( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{5} + 27 x + 3$ $3$ $2$ $9$ $44$ $C_3\times D_9$ (as 18T19) not computed not computed $[2, 3]$ $[1,2]$ not computed not computed not computed not computed $t^{2} + 2 t + 2$ $x^{9} + \left(18 t + 18\right) x^{8} + 3 x^{6} + 18 x^{5} + 54 t + 3$ $[14, 6, 0]$ $[1, 1]$ $z^6 + 2,2 z^2 + 2$ undefined
3.1.18.37c2.165 $x^{18} + 18 x^{9} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 9 x^{5} + 9 x^{4} + 9 x^{2} + 6$ $3$ $1$ $18$ $37$ $C_3\times D_9$ (as 18T19) not computed not computed $[\frac{3}{2}, \frac{5}{2}]$ $[\frac{1}{2},\frac{3}{2}]$ not computed not computed not computed not computed $t + 1$ $x^{18} + 18 x^{9} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 9 x^{5} + 9 x^{4} + 9 x^{2} + 6$ $[20, 6, 0]$ $[1, 1, 1]$ $z^9 + 2,2 z^6 + 1,z^2 + 2$ undefined
3.1.18.53a1.34 $x^{18} + 27 x^{9} + 27 x^{8} + 54 x^{4} + 3$ $3$ $1$ $18$ $53$ $C_3\times D_9$ (as 18T19) not computed not computed $[\frac{5}{2}, \frac{7}{2}]$ $[\frac{3}{2},\frac{5}{2}]$ not computed not computed not computed not computed $t + 1$ $x^{18} + 27 x^{9} + 27 x^{8} + 54 x^{4} + 3$ $[36, 18, 0]$ $[1, 1, 1]$ $z^9 + 2,2 z^6 + 1,z^2 + 2$ $[1, 7, 25]$
3.1.18.53a1.36 $x^{18} + 27 x^{9} + 54 x^{8} + 54 x^{4} + 3$ $3$ $1$ $18$ $53$ $C_3\times D_9$ (as 18T19) not computed not computed $[\frac{5}{2}, \frac{7}{2}]$ $[\frac{3}{2},\frac{5}{2}]$ not computed not computed not computed not computed $t + 1$ $x^{18} + 27 x^{9} + 54 x^{8} + 54 x^{4} + 3$ $[36, 18, 0]$ $[1, 1, 1]$ $z^9 + 2,2 z^6 + 1,z^2 + 2$ $[1, 7, 25]$
3.1.18.53a1.40 $x^{18} + 27 x^{8} + 27 x^{7} + 54 x^{4} + 3$ $3$ $1$ $18$ $53$ $C_3\times D_9$ (as 18T19) not computed not computed $[\frac{5}{2}, \frac{7}{2}]$ $[\frac{3}{2},\frac{5}{2}]$ not computed not computed not computed not computed $t + 1$ $x^{18} + 27 x^{8} + 27 x^{7} + 54 x^{4} + 3$ $[36, 18, 0]$ $[1, 1, 1]$ $z^9 + 2,2 z^6 + 1,z^2 + 2$ $[1, 7, 25]$
3.1.18.53a1.41 $x^{18} + 27 x^{9} + 27 x^{8} + 27 x^{7} + 54 x^{4} + 3$ $3$ $1$ $18$ $53$ $C_3\times D_9$ (as 18T19) not computed not computed $[\frac{5}{2}, \frac{7}{2}]$ $[\frac{3}{2},\frac{5}{2}]$ not computed not computed not computed not computed $t + 1$ $x^{18} + 27 x^{9} + 27 x^{8} + 27 x^{7} + 54 x^{4} + 3$ $[36, 18, 0]$ $[1, 1, 1]$ $z^9 + 2,2 z^6 + 1,z^2 + 2$ $[1, 7, 25]$
3.1.18.53a1.42 $x^{18} + 54 x^{9} + 27 x^{8} + 27 x^{7} + 54 x^{4} + 3$ $3$ $1$ $18$ $53$ $C_3\times D_9$ (as 18T19) not computed not computed $[\frac{5}{2}, \frac{7}{2}]$ $[\frac{3}{2},\frac{5}{2}]$ not computed not computed not computed not computed $t + 1$ $x^{18} + 54 x^{9} + 27 x^{8} + 27 x^{7} + 54 x^{4} + 3$ $[36, 18, 0]$ $[1, 1, 1]$ $z^9 + 2,2 z^6 + 1,z^2 + 2$ $[1, 7, 25]$
17.2.9.16a1.4 $( x^{2} + 16 x + 3 )^{9} + 255 x + 238$ $17$ $2$ $9$ $16$ $C_3\times D_9$ (as 18T19) $6$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}^{6}$ $[\ ]_{9}^{6}$ $[\ ]^{3}$ $[\ ]^{3}$ $t^{2} + 16 t + 3$ $x^{9} + 255 t + 238$ $[0]$ $[1]$ $z^8 + 9 z^7 + 2 z^6 + 16 z^5 + 7 z^4 + 7 z^3 + 16 z^2 + 2 z + 9$ undefined
53.2.9.16a1.4 $( x^{2} + 49 x + 2 )^{9} + 742 x + 2385$ $53$ $2$ $9$ $16$ $C_3\times D_9$ (as 18T19) $6$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}^{6}$ $[\ ]_{9}^{6}$ $[\ ]^{3}$ $[\ ]^{3}$ $t^{2} + 49 t + 2$ $x^{9} + 1590 t + 2279$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 31 z^5 + 20 z^4 + 20 z^3 + 31 z^2 + 36 z + 9$ undefined
71.2.9.16a1.4 $( x^{2} + 69 x + 7 )^{9} + 2201 x + 4402$ $71$ $2$ $9$ $16$ $C_3\times D_9$ (as 18T19) $6$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}^{6}$ $[\ ]_{9}^{6}$ $[\ ]^{3}$ $[\ ]^{3}$ $t^{2} + 69 t + 7$ $x^{9} + 4828 t + 4047$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 13 z^5 + 55 z^4 + 55 z^3 + 13 z^2 + 36 z + 9$ undefined
89.2.9.16a1.3 $( x^{2} + 82 x + 3 )^{9} + 4094 x + 6052$ $89$ $2$ $9$ $16$ $C_3\times D_9$ (as 18T19) $6$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}^{6}$ $[\ ]_{9}^{6}$ $[\ ]^{3}$ $[\ ]^{3}$ $t^{2} + 82 t + 3$ $x^{9} + 4094 t + 6052$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 84 z^5 + 37 z^4 + 37 z^3 + 84 z^2 + 36 z + 9$ undefined
107.2.9.16a1.4 $( x^{2} + 103 x + 2 )^{9} + 1498 x + 10593$ $107$ $2$ $9$ $16$ $C_3\times D_9$ (as 18T19) $6$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}^{6}$ $[\ ]_{9}^{6}$ $[\ ]^{3}$ $[\ ]^{3}$ $t^{2} + 103 t + 2$ $x^{9} + 1498 t + 10593$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 84 z^5 + 19 z^4 + 19 z^3 + 84 z^2 + 36 z + 9$ undefined
179.2.9.16a1.3 $( x^{2} + 172 x + 2 )^{9} + 1074 x + 13246$ $179$ $2$ $9$ $16$ $C_3\times D_9$ (as 18T19) $6$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}^{6}$ $[\ ]_{9}^{6}$ $[\ ]^{3}$ $[\ ]^{3}$ $t^{2} + 172 t + 2$ $x^{9} + 8413 t + 29535$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 84 z^5 + 126 z^4 + 126 z^3 + 84 z^2 + 36 z + 9$ undefined
197.2.9.16a1.3 $( x^{2} + 192 x + 2 )^{9} + 3546 x + 5319$ $197$ $2$ $9$ $16$ $C_3\times D_9$ (as 18T19) $6$ $9$ $[\ ]$ $[\ ]$ $[\ ]_{9}^{6}$ $[\ ]_{9}^{6}$ $[\ ]^{3}$ $[\ ]^{3}$ $t^{2} + 192 t + 2$ $x^{9} + 3546 t + 5319$ $[0]$ $[1]$ $z^8 + 9 z^7 + 36 z^6 + 84 z^5 + 126 z^4 + 126 z^3 + 84 z^2 + 36 z + 9$ undefined
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