↑

Learn more

Note: Search results may be incomplete due to uncomputed quantities: Hidden content (1054941 objects)

Refine search

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
Family Hidden content
Sort order Select

Results (displaying both matches)

  displayed columns for results
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
5.4.2.4a1.1 $( x^{4} + 4 x^{2} + 4 x + 2 )^{2} + 5 x$ $5$ $4$ $2$ $4$ $C_8$ (as 8T1) $4$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{4}$ $[\ ]_{2}^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 4 t^{2} + 4 t + 2$ $x^{2} + 5 t$ $[0]$ $[1]$ $z + 2$ undefined
5.4.2.4a1.2 $( x^{4} + 4 x^{2} + 4 x + 2 )^{2} + 5$ $5$ $4$ $2$ $4$ $C_4\times C_2$ (as 8T2) $4$ $2$ $[\ ]$ $[\ ]$ $[\ ]_{2}^{4}$ $[\ ]_{2}^{4}$ $[\ ]$ $[\ ]$ $t^{4} + 4 t^{2} + 4 t + 2$ $x^{2} + 5$ $[0]$ $[1]$ $z + 2$ undefined
  displayed columns for results