Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q7 of degree 7

j Ramification Polygon Slopes Residual Polynomials #A Polynomials Extensions
1{(1,1), (7,0)}[ 1/6 ](z+1)66424242
2{(1,2), (7,0)}[ 1/3 ](z2+1)33214242
(z2+3)3321
3{(1,3), (7,0)}[ 1/2 ](z3+1)22144242
(z3+2)2214
(z3+3)2214
4{(1,4), (7,0)}[ 2/3 ](z2+1)33214242
(z2+3)3321
5{(1,5), (7,0)}[ 5/6 ](z+1)66424242
6{(1,6), (7,0)}[ 1 ](z6+1)1174242
(z6+2)117
(z6+3)117
(z6+4)117
(z6+5)117
(z6+6)177
7{(1,7), (7,0)}[ 7/6 ](z+6)17494949