Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q2 of degree 4

j Ramification Polygon Slopes Residual Polynomials #A Polynomials Extensions
1{(1,1), (4,0)}[ 1/3 ](z+1)11444
3{(1,3), (4,0)}[ 1 ](z3+1)12448
{(1,3), (2,2), (4,0)}[ 1 ](z3+z+1)1144
5{(1,5), (4,0)}[ 5/3 ](z+1)128816
{(1,5), (2,2), (4,0)}[ 3, 1 ](z+1, z2+1)18 [!]88
6{(1,6), (2,2), (4,0)}[ 4, 1 ](z+1, z2+1)116 [!]161616
7{(1,7), (2,4), (4,0)}[ 3, 2 ](z+1, z2+1)116 [!]161616
8{(1,8), (2,4), (4,0)}[ 4, 2 ](z+1, z2+1)132 [!]323232