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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 (4 matches)

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Label Polynomial $p$ $e$ $f$ $c$ Galois group Visible slopes Slope content Unram. Ext. Eisen. Poly.
2.15.0.1 $x^{15} + x^{5} + x^{4} + x^{2} + 1$ $2$ $1$ $15$ $0$ $C_{15}$ (as 15T1) $[\ ]$ $[\ ]^{15}$ $t^{15} + t^{5} + t^{4} + t^{2} + 1$ $x - 2$
2.15.10.1 $x^{15} + 13 x^{12} + 3 x^{10} + 13 x^{9} - 174 x^{7} - 45 x^{6} + 3 x^{5} + 513 x^{4} + 63 x^{2} - 216 x + 109$ $2$ $3$ $5$ $10$ $S_3 \times C_5$ (as 15T4) $[\ ]$ $[\ ]_{3}^{10}$ $t^{5} + t^{2} + 1$ $x^{3} + 2$
2.15.12.1 $x^{15} + 5 x^{13} + 5 x^{12} + 10 x^{11} + 26 x^{10} + 20 x^{9} - 145 x^{7} + 70 x^{6} + 73 x^{5} + 315 x^{4} - 105 x^{3} + 200 x^{2} + 5 x + 1$ $2$ $5$ $3$ $12$ $F_5\times C_3$ (as 15T8) $[\ ]$ $[\ ]_{5}^{12}$ $t^{3} + t + 1$ $x^{5} + 2$
2.15.14.1 $x^{15} + 2$ $2$ $15$ $1$ $14$ $C_{15} : C_4$ (as 15T6) $[\ ]$ $[\ ]_{15}^{4}$ $t + 1$ $x^{15} + 2$
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