Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q5 of degree 5

j Ramification Polygon Slopes Residual Polynomials #A Polynomials Extensions
1{(1,1), (5,0)}[ 1/4 ](z+1)44202020
2{(1,2), (5,0)}[ 1/2 ](z2+1)22102020
(z2+2)2210
3{(1,3), (5,0)}[ 3/4 ](z+1)44202020
4{(1,4), (5,0)}[ 1 ](z4+1)1152020
(z4+2)115
(z4+3)115
(z4+4)155
5{(1,5), (5,0)}[ 5/4 ](z+4)15252525