Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q2 of degree 14

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), (14,0)}[ 1, 0 ](z+1, z12+1){2}37{ 168, 336 }{ 14T18, 14T11 }27·27·27·2
3{(1,3), (2,0), (14,0)}[ 3, 0 ](z+1, z12+1){2}37{ 168, 336, 1344, 2688 }{ 14T35, 14T18, 14T11, 14T44 }227·227·227·22
5{(1,5), (2,0), (14,0)}[ 5, 0 ](z+1, z12+1){2}37{ 168, 336, 1344, 2688 }{ 14T35, 14T18, 14T11, 14T44 }237·237·237·23
7{(1,7), (2,0), (14,0)}[ 7, 0 ](z+1, z12+1){2}37{ 42, 336, 2688 }{ 14T5, 14T18, 14T44 }247·247·247·24
9{(1,9), (2,0), (14,0)}[ 9, 0 ](z+1, z12+1){2}37{ 168, 336, 1344, 2688 }{ 14T35, 14T18, 14T11, 14T44 }257·257·257·25
11{(1,11), (2,0), (14,0)}[ 11, 0 ](z+1, z12+1){2}37{ 168, 336, 1344, 2688 }{ 14T35, 14T18, 14T11, 14T44 }267·267·267·26
13{(1,13), (2,0), (14,0)}[ 13, 0 ](z+1, z12+1){2}37{ 168, 336, 1344, 2688 }{ 14T35, 14T18, 14T11, 14T44 }277·277·277·27
14{(1,14), (2,0), (14,0)}[ 14, 0 ](z+1, z12+1){2}37{ 42, 336, 2688 }{ 14T5, 14T18, 14T44 }28 [.]7·287·287·28