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Degree Residue characteristic Galois group Galois unramified degree Assoc. Inertia
Ramification index Discriminant exponent Inertia subgroup Galois tame degree Indices
Residue field degree Top slope Wild Visible Wild inertia subgroup
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Results (18 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group $u$ $t$ Visible slopes Slope content Unram. Ext. Eisen. Poly. Ind. of Insep. Assoc. Inertia
11.10.0.1 $x^{10} + 7 x^{5} + 8 x^{4} + 10 x^{3} + 6 x^{2} + 6 x + 2$ $11$ $1$ $10$ $0$ $C_{10}$ (as 10T1) $10$ $1$ $[\ ]$ $[\ ]^{10}$ $t^{10} + 7 t^{5} + 8 t^{4} + 10 t^{3} + 6 t^{2} + 6 t + 2$ $x - 11$ $[0]$ $[\ ]$
11.10.5.1 $x^{10} - 13310 x^{4} - 1449459$ $11$ $2$ $5$ $5$ $C_{10}$ (as 10T1) $5$ $2$ $[\ ]$ $[\ ]_{2}^{5}$ $t^{5} + 10 t^{2} + 9$ $x^{2} + 11 t$ $[0]$ $[1]$
11.10.5.2 $x^{10} + 55 x^{8} + 20 x^{7} + 1210 x^{6} - 202 x^{5} + 13410 x^{4} - 14080 x^{3} + 75585 x^{2} - 68970 x + 171252$ $11$ $2$ $5$ $5$ $C_{10}$ (as 10T1) $5$ $2$ $[\ ]$ $[\ ]_{2}^{5}$ $t^{5} + 10 t^{2} + 9$ $x^{2} + 11$ $[0]$ $[1]$
11.10.8.1 $x^{10} - 77 x^{5} + 242$ $11$ $5$ $2$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]_{5}^{2}$ $t^{2} + 7 t + 2$ $x^{5} + 11 t$ $[0]$ $[1]$
11.10.8.2 $x^{10} - 198 x^{5} - 10043$ $11$ $5$ $2$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]_{5}^{2}$ $t^{2} + 7 t + 2$ $x^{5} + 44 t + 55$ $[0]$ $[1]$
11.10.8.3 $x^{10} - 110 x^{5} - 16819$ $11$ $5$ $2$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]_{5}^{2}$ $t^{2} + 7 t + 2$ $x^{5} + 44 t + 99$ $[0]$ $[1]$
11.10.8.4 $x^{10} - 165 x^{5} - 4356$ $11$ $5$ $2$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]_{5}^{2}$ $t^{2} + 7 t + 2$ $x^{5} + 33 t + 33$ $[0]$ $[1]$
11.10.8.5 $x^{10} + 35 x^{9} + 500 x^{8} + 3710 x^{7} + 14985 x^{6} + 31389 x^{5} + 30355 x^{4} + 19790 x^{3} + 37110 x^{2} + 111495 x + 148840$ $11$ $5$ $2$ $8$ $C_{10}$ (as 10T1) $2$ $5$ $[\ ]$ $[\ ]_{5}^{2}$ $t^{2} + 7 t + 2$ $x^{5} + 11$ $[0]$ $[1]$
11.10.9.1 $x^{10} + 110$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 110$ $[0]$ $[1]$
11.10.9.2 $x^{10} + 66$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 66$ $[0]$ $[1]$
11.10.9.3 $x^{10} + 77$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 77$ $[0]$ $[1]$
11.10.9.4 $x^{10} + 22$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 22$ $[0]$ $[1]$
11.10.9.5 $x^{10} + 88$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 88$ $[0]$ $[1]$
11.10.9.6 $x^{10} + 44$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 44$ $[0]$ $[1]$
11.10.9.7 $x^{10} + 11$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 11$ $[0]$ $[1]$
11.10.9.8 $x^{10} + 33$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 33$ $[0]$ $[1]$
11.10.9.9 $x^{10} + 55$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 55$ $[0]$ $[1]$
11.10.9.10 $x^{10} + 99$ $11$ $10$ $1$ $9$ $C_{10}$ (as 10T1) $1$ $10$ $[\ ]$ $[\ ]_{10}$ $t + 9$ $x^{10} + 99$ $[0]$ $[1]$
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