Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q3 of degree 6

j Ramification Polygon Slopes Residual Polynomials #A Polynomials Extensions
1{(1,1), (3,0), (6,0)}[ 1/2, 0 ](2z+1, z3+2)22121212
2{(1,2), (3,0), (6,0)}[ 1, 0 ](2z2+1, z3+2)1361212
(2z2+2, z3+2)116
4{(1,4), (3,0), (6,0)}[ 2, 0 ](2z2+1, z3+2)19183636
(2z2+2, z3+2)1318
5{(1,5), (3,0), (6,0)}[ 5/2, 0 ](2z+1, z3+2)26363636
6{(1,6), (3,0), (6,0)}[ 3, 0 ](2z2+1, z3+2)127545454