Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q11 of degree 11

Introduction

Polynomial Invariants #Aut Splitting Field Number of
j Ramification Polygon Slopes Residual Polynomials fT eT #Gal Gal Polynomials Extensions
1{(1,1), (11,0)}[ 1/10 ](z+1){1}110{ 110 }{ 11T4 }11110·1110·11
(z+2){1}110{ 110 }{ 11T4 }111
(z+3){1}110{ 110 }{ 11T4 }111
(z+4){1}110{ 110 }{ 11T4 }111
(z+5){1}110{ 110 }{ 11T4 }111
(z+6){1}110{ 110 }{ 11T4 }111
(z+7){1}110{ 110 }{ 11T4 }111
(z+8){1}110{ 110 }{ 11T4 }111
(z+9){1}110{ 110 }{ 11T4 }111
(z+10){1}110{ 110 }{ 11T4 }111
2{(1,2), (11,0)}[ 1/5 ](z2+1){1}25{ 110 }{ 11T4 }11110·1110·11
(z2+2){1}15{ 55 }{ 11T3 }111
(z2+3){1}25{ 110 }{ 11T4 }111
(z2+4){1}25{ 110 }{ 11T4 }111
(z2+5){1}25{ 110 }{ 11T4 }111
(z2+6){1}15{ 55 }{ 11T3 }111
(z2+7){1}15{ 55 }{ 11T3 }111
(z2+8){1}15{ 55 }{ 11T3 }111
(z2+9){1}25{ 110 }{ 11T4 }111
(z2+10){1}15{ 55 }{ 11T3 }111
3{(1,3), (11,0)}[ 3/10 ](z+1){1}110{ 110 }{ 11T4 }11110·1110·11
(z+2){1}110{ 110 }{ 11T4 }111
(z+3){1}110{ 110 }{ 11T4 }111
(z+4){1}110{ 110 }{ 11T4 }111
(z+5){1}110{ 110 }{ 11T4 }111
(z+6){1}110{ 110 }{ 11T4 }111
(z+7){1}110{ 110 }{ 11T4 }111
(z+8){1}110{ 110 }{ 11T4 }111
(z+9){1}110{ 110 }{ 11T4 }111
(z+10){1}110{ 110 }{ 11T4 }111
4{(1,4), (11,0)}[ 2/5 ](z2+1){1}25{ 110 }{ 11T4 }11110·1110·11
(z2+2){1}15{ 55 }{ 11T3 }111
(z2+3){1}25{ 110 }{ 11T4 }111
(z2+4){1}25{ 110 }{ 11T4 }111
(z2+5){1}25{ 110 }{ 11T4 }111
(z2+6){1}15{ 55 }{ 11T3 }111
(z2+7){1}15{ 55 }{ 11T3 }111
(z2+8){1}15{ 55 }{ 11T3 }111
(z2+9){1}25{ 110 }{ 11T4 }111
(z2+10){1}15{ 55 }{ 11T3 }111
5{(1,5), (11,0)}[ 1/2 ](z5+1){1}12{ 22 }{ 11T2 }11110·1110·11
(z5+2){1}52{ 110 }{ 11T4 }111
(z5+3){1}52{ 110 }{ 11T4 }111
(z5+4){1}52{ 110 }{ 11T4 }111
(z5+5){1}52{ 110 }{ 11T4 }111
(z5+6){1}52{ 110 }{ 11T4 }111
(z5+7){1}52{ 110 }{ 11T4 }111
(z5+8){1}52{ 110 }{ 11T4 }111
(z5+9){1}52{ 110 }{ 11T4 }111
(z5+10){1}12{ 22 }{ 11T2 }111
6{(1,6), (11,0)}[ 3/5 ](z2+1){1}25{ 110 }{ 11T4 }11110·1110·11
(z2+2){1}15{ 55 }{ 11T3 }111
(z2+3){1}25{ 110 }{ 11T4 }111
(z2+4){1}25{ 110 }{ 11T4 }111
(z2+5){1}25{ 110 }{ 11T4 }111
(z2+6){1}15{ 55 }{ 11T3 }111
(z2+7){1}15{ 55 }{ 11T3 }111
(z2+8){1}15{ 55 }{ 11T3 }111
(z2+9){1}25{ 110 }{ 11T4 }111
(z2+10){1}15{ 55 }{ 11T3 }111
7{(1,7), (11,0)}[ 7/10 ](z+1){1}110{ 110 }{ 11T4 }11110·1110·11
(z+2){1}110{ 110 }{ 11T4 }111
(z+3){1}110{ 110 }{ 11T4 }111
(z+4){1}110{ 110 }{ 11T4 }111
(z+5){1}110{ 110 }{ 11T4 }111
(z+6){1}110{ 110 }{ 11T4 }111
(z+7){1}110{ 110 }{ 11T4 }111
(z+8){1}110{ 110 }{ 11T4 }111
(z+9){1}110{ 110 }{ 11T4 }111
(z+10){1}110{ 110 }{ 11T4 }111
8{(1,8), (11,0)}[ 4/5 ](z2+1){1}25{ 110 }{ 11T4 }11110·1110·11
(z2+2){1}15{ 55 }{ 11T3 }111
(z2+3){1}25{ 110 }{ 11T4 }111
(z2+4){1}25{ 110 }{ 11T4 }111
(z2+5){1}25{ 110 }{ 11T4 }111
(z2+6){1}15{ 55 }{ 11T3 }111
(z2+7){1}15{ 55 }{ 11T3 }111
(z2+8){1}15{ 55 }{ 11T3 }111
(z2+9){1}25{ 110 }{ 11T4 }111
(z2+10){1}15{ 55 }{ 11T3 }111
9{(1,9), (11,0)}[ 9/10 ](z+1){1}110{ 110 }{ 11T4 }11110·1110·11
(z+2){1}110{ 110 }{ 11T4 }111
(z+3){1}110{ 110 }{ 11T4 }111
(z+4){1}110{ 110 }{ 11T4 }111
(z+5){1}110{ 110 }{ 11T4 }111
(z+6){1}110{ 110 }{ 11T4 }111
(z+7){1}110{ 110 }{ 11T4 }111
(z+8){1}110{ 110 }{ 11T4 }111
(z+9){1}110{ 110 }{ 11T4 }111
(z+10){1}110{ 110 }{ 11T4 }111
10{(1,10), (11,0)}[ 1 ](z10+1){1}21{ 22 }{ 11T2 }11110·1110·11
(z10+2){1}51{ 55 }{ 11T3 }111
(z10+3){1}101{ 110 }{ 11T4 }111
(z10+4){1}101{ 110 }{ 11T4 }111
(z10+5){1}101{ 110 }{ 11T4 }111
(z10+6){1}51{ 55 }{ 11T3 }111
(z10+7){1}51{ 55 }{ 11T3 }111
(z10+8){1}51{ 55 }{ 11T3 }111
(z10+9){1}101{ 110 }{ 11T4 }111
(z10+10){11}11{ 11 }{ 11T1 }1111
11{(1,11), (11,0)}[ 11/10 ](z+10){1}110{ 110 }{ 11T4 }11112112112