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 Num. automorphisms
Ramification index $e$ Residue field degree $f$ Galois tame degree $t$ Galois unram. degree $u$ Intermediate field
Inertia subgroup Indices Assoc. Inertia Jump Set
Top Artin slope Galois Artin Visible Artin Wild inertia subgroup
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Results (1-50 of 101 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
2.11.1.0a1.1 $x^{11} + x^{2} + 1$ $2$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + t^{2} + 1$ $x - 2$ $[0]$ $[\ ]$ $[1]$
3.11.1.0a1.1 $x^{11} + 2 x^{2} + 1$ $3$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 2 t^{2} + 1$ $x - 3$ $[0]$ $[\ ]$ undefined
5.11.1.0a1.1 $x^{11} + 3 x + 3$ $5$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 3 t + 3$ $x - 5$ $[0]$ $[\ ]$ undefined
7.11.1.0a1.1 $x^{11} + x + 4$ $7$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + t + 4$ $x - 7$ $[0]$ $[\ ]$ undefined
11.11.1.0a1.1 $x^{11} + 10 x + 9$ $11$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 10 t + 9$ $x - 11$ $[0]$ $[\ ]$ undefined
11.1.11.20a10.1 $x^{11} + 110 x^{10} + 11$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 11$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.2 $x^{11} + 110 x^{10} + 132$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 132$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.3 $x^{11} + 110 x^{10} + 253$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 253$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.4 $x^{11} + 110 x^{10} + 374$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 374$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.5 $x^{11} + 110 x^{10} + 495$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 495$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.6 $x^{11} + 110 x^{10} + 616$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 616$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.7 $x^{11} + 110 x^{10} + 737$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 737$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.8 $x^{11} + 110 x^{10} + 858$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 858$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.9 $x^{11} + 110 x^{10} + 979$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 979$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.10 $x^{11} + 110 x^{10} + 1100$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 1100$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
11.1.11.20a10.11 $x^{11} + 110 x^{10} + 1221$ $11$ $1$ $11$ $20$ $C_{11}$ (as 11T1) $1$ $1$ $[2]$ $[1]$ $[2]$ $[1]$ $[\ ]$ $[\ ]$ $t + 9$ $x^{11} + 110 x^{10} + 1221$ $[10, 0]$ $[1]$ $z^{10} + 10$ undefined
13.11.1.0a1.1 $x^{11} + 3 x + 11$ $13$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 3 t + 11$ $x - 13$ $[0]$ $[\ ]$ undefined
17.11.1.0a1.1 $x^{11} + 5 x + 14$ $17$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 5 t + 14$ $x - 17$ $[0]$ $[\ ]$ undefined
19.11.1.0a1.1 $x^{11} + 8 x + 17$ $19$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 8 t + 17$ $x - 19$ $[0]$ $[\ ]$ undefined
23.11.1.0a1.1 $x^{11} + 22 x^{2} + 7 x + 18$ $23$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 22 t^{2} + 7 t + 18$ $x - 23$ $[0]$ $[\ ]$ undefined
23.1.11.10a1.1 $x^{11} + 23$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 23$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.2 $x^{11} + 46$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 46$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.3 $x^{11} + 92$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 92$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.4 $x^{11} + 115$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 115$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.5 $x^{11} + 184$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 184$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.6 $x^{11} + 207$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 207$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.7 $x^{11} + 230$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 230$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.8 $x^{11} + 253$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 253$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.9 $x^{11} + 368$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 368$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.10 $x^{11} + 391$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 391$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
23.1.11.10a1.11 $x^{11} + 460$ $23$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 18$ $x^{11} + 460$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 9 z^8 + 4 z^7 + 8 z^6 + 2 z^5 + 2 z^4 + 8 z^3 + 4 z^2 + 9 z + 11$ undefined
29.11.1.0a1.1 $x^{11} + 28 x^{2} + 8 x + 27$ $29$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 28 t^{2} + 8 t + 27$ $x - 29$ $[0]$ $[\ ]$ undefined
31.11.1.0a1.1 $x^{11} + 20 x + 28$ $31$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 20 t + 28$ $x - 31$ $[0]$ $[\ ]$ undefined
37.11.1.0a1.1 $x^{11} + 2 x + 35$ $37$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 2 t + 35$ $x - 37$ $[0]$ $[\ ]$ undefined
41.11.1.0a1.1 $x^{11} + 20 x + 35$ $41$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 20 t + 35$ $x - 41$ $[0]$ $[\ ]$ undefined
43.11.1.0a1.1 $x^{11} + 7 x + 40$ $43$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 7 t + 40$ $x - 43$ $[0]$ $[\ ]$ undefined
47.11.1.0a1.1 $x^{11} + 6 x + 42$ $47$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 6 t + 42$ $x - 47$ $[0]$ $[\ ]$ undefined
53.11.1.0a1.1 $x^{11} + 15 x + 51$ $53$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 15 t + 51$ $x - 53$ $[0]$ $[\ ]$ undefined
59.11.1.0a1.1 $x^{11} + 6 x + 57$ $59$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 6 t + 57$ $x - 59$ $[0]$ $[\ ]$ undefined
61.11.1.0a1.1 $x^{11} + 18 x + 59$ $61$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 18 t + 59$ $x - 61$ $[0]$ $[\ ]$ undefined
67.11.1.0a1.1 $x^{11} + 66 x^{2} + 9 x + 65$ $67$ $11$ $1$ $0$ $C_{11}$ (as 11T1) $11$ $1$ $[\ ]$ $[\ ]$ $[\ ]^{11}$ $[\ ]^{11}$ $[\ ]$ $[\ ]$ $t^{11} + 66 t^{2} + 9 t + 65$ $x - 67$ $[0]$ $[\ ]$ undefined
67.1.11.10a1.1 $x^{11} + 67$ $67$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 65$ $x^{11} + 67$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 55 z^8 + 31 z^7 + 62 z^6 + 60 z^5 + 60 z^4 + 62 z^3 + 31 z^2 + 55 z + 11$ undefined
67.1.11.10a1.2 $x^{11} + 134$ $67$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 65$ $x^{11} + 134$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 55 z^8 + 31 z^7 + 62 z^6 + 60 z^5 + 60 z^4 + 62 z^3 + 31 z^2 + 55 z + 11$ undefined
67.1.11.10a1.3 $x^{11} + 268$ $67$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 65$ $x^{11} + 268$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 55 z^8 + 31 z^7 + 62 z^6 + 60 z^5 + 60 z^4 + 62 z^3 + 31 z^2 + 55 z + 11$ undefined
67.1.11.10a1.4 $x^{11} + 536$ $67$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 65$ $x^{11} + 536$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 55 z^8 + 31 z^7 + 62 z^6 + 60 z^5 + 60 z^4 + 62 z^3 + 31 z^2 + 55 z + 11$ undefined
67.1.11.10a1.5 $x^{11} + 1072$ $67$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 65$ $x^{11} + 1072$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 55 z^8 + 31 z^7 + 62 z^6 + 60 z^5 + 60 z^4 + 62 z^3 + 31 z^2 + 55 z + 11$ undefined
67.1.11.10a1.6 $x^{11} + 1273$ $67$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 65$ $x^{11} + 1273$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 55 z^8 + 31 z^7 + 62 z^6 + 60 z^5 + 60 z^4 + 62 z^3 + 31 z^2 + 55 z + 11$ undefined
67.1.11.10a1.7 $x^{11} + 2144$ $67$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 65$ $x^{11} + 2144$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 55 z^8 + 31 z^7 + 62 z^6 + 60 z^5 + 60 z^4 + 62 z^3 + 31 z^2 + 55 z + 11$ undefined
67.1.11.10a1.8 $x^{11} + 2881$ $67$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 65$ $x^{11} + 2881$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 55 z^8 + 31 z^7 + 62 z^6 + 60 z^5 + 60 z^4 + 62 z^3 + 31 z^2 + 55 z + 11$ undefined
67.1.11.10a1.9 $x^{11} + 3685$ $67$ $1$ $11$ $10$ $C_{11}$ (as 11T1) $1$ $11$ $[\ ]$ $[\ ]$ $[\ ]_{11}$ $[\ ]_{11}$ $[\ ]$ $[\ ]$ $t + 65$ $x^{11} + 3685$ $[0]$ $[1]$ $z^{10} + 11 z^9 + 55 z^8 + 31 z^7 + 62 z^6 + 60 z^5 + 60 z^4 + 62 z^3 + 31 z^2 + 55 z + 11$ undefined
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