Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q2 of degree 6

Introduction

Polynomial Invariants #Aut Splitting Field Number of
j Ramification Polygon Slopes Residual Polynomials fT eT #Gal Gal Polynomials Extensions
1{(1,1), (2,0), (6,0)}[ 1, 0 ](z+1, z4+1){2}23{ 24 }{ 6T8, 6T7 }23·23·23·2
3{(1,3), (2,0), (6,0)}[ 3, 0 ](z+1, z4+1){2}23{ 12, 48 }{ 6T11, 6T3 }223·223·223·22
5{(1,5), (2,0), (6,0)}[ 5, 0 ](z+1, z4+1){2}23{ 24, 48 }{ 6T8, 6T11, 6T7 }233·233·233·23
6{(1,6), (2,0), (6,0)}[ 6, 0 ](z+1, z4+1){2}23{ 12, 48 }{ 6T11, 6T3 }24 [.]3·243·243·24