Number Theory Tables, Department of Mathematics and Statistics, UNCG

Number of totally ramified extensions of Q13 of degree 13

Introduction

Polynomial Invariants #Aut Splitting Field Number of
j Ramification Polygon Slopes Residual Polynomials fT eT #Gal Gal Polynomials Extensions
1{(1,1), (13,0)}[ 1/12 ](z+1){1}112{ 156 }{ 13T6 }11312·1312·13
(z+2){1}112{ 156 }{ 13T6 }113
(z+3){1}112{ 156 }{ 13T6 }113
(z+4){1}112{ 156 }{ 13T6 }113
(z+5){1}112{ 156 }{ 13T6 }113
(z+6){1}112{ 156 }{ 13T6 }113
(z+7){1}112{ 156 }{ 13T6 }113
(z+8){1}112{ 156 }{ 13T6 }113
(z+9){1}112{ 156 }{ 13T6 }113
(z+10){1}112{ 156 }{ 13T6 }113
(z+11){1}112{ 156 }{ 13T6 }113
(z+12){1}112{ 156 }{ 13T6 }113
2{(1,2), (13,0)}[ 1/6 ](z2+1){1}16{ 78 }{ 13T5 }11312·1312·13
(z2+2){1}26{ 156 }{ 13T6 }113
(z2+3){1}16{ 78 }{ 13T5 }113
(z2+4){1}16{ 78 }{ 13T5 }113
(z2+5){1}26{ 156 }{ 13T6 }113
(z2+6){1}26{ 156 }{ 13T6 }113
(z2+7){1}26{ 156 }{ 13T6 }113
(z2+8){1}26{ 156 }{ 13T6 }113
(z2+9){1}16{ 78 }{ 13T5 }113
(z2+10){1}16{ 78 }{ 13T5 }113
(z2+11){1}26{ 156 }{ 13T6 }113
(z2+12){1}16{ 78 }{ 13T5 }113
3{(1,3), (13,0)}[ 1/4 ](z3+1){1}14{ 52 }{ 13T4 }11312·1312·13
(z3+2){1}34{ 156 }{ 13T6 }113
(z3+3){1}34{ 156 }{ 13T6 }113
(z3+4){1}34{ 156 }{ 13T6 }113
(z3+5){1}14{ 52 }{ 13T4 }113
(z3+6){1}34{ 156 }{ 13T6 }113
(z3+7){1}34{ 156 }{ 13T6 }113
(z3+8){1}14{ 52 }{ 13T4 }113
(z3+9){1}34{ 156 }{ 13T6 }113
(z3+10){1}34{ 156 }{ 13T6 }113
(z3+11){1}34{ 156 }{ 13T6 }113
(z3+12){1}14{ 52 }{ 13T4 }113
4{(1,4), (13,0)}[ 1/3 ](z4+1){1}23{ 78 }{ 13T5 }11312·1312·13
(z4+2){1}43{ 156 }{ 13T6 }113
(z4+3){1}23{ 78 }{ 13T5 }113
(z4+4){1}13{ 39 }{ 13T3 }113
(z4+5){1}43{ 156 }{ 13T6 }113
(z4+6){1}43{ 156 }{ 13T6 }113
(z4+7){1}43{ 156 }{ 13T6 }113
(z4+8){1}43{ 156 }{ 13T6 }113
(z4+9){1}23{ 78 }{ 13T5 }113
(z4+10){1}13{ 39 }{ 13T3 }113
(z4+11){1}43{ 156 }{ 13T6 }113
(z4+12){1}13{ 39 }{ 13T3 }113
5{(1,5), (13,0)}[ 5/12 ](z+1){1}112{ 156 }{ 13T6 }11312·1312·13
(z+2){1}112{ 156 }{ 13T6 }113
(z+3){1}112{ 156 }{ 13T6 }113
(z+4){1}112{ 156 }{ 13T6 }113
(z+5){1}112{ 156 }{ 13T6 }113
(z+6){1}112{ 156 }{ 13T6 }113
(z+7){1}112{ 156 }{ 13T6 }113
(z+8){1}112{ 156 }{ 13T6 }113
(z+9){1}112{ 156 }{ 13T6 }113
(z+10){1}112{ 156 }{ 13T6 }113
(z+11){1}112{ 156 }{ 13T6 }113
(z+12){1}112{ 156 }{ 13T6 }113
6{(1,6), (13,0)}[ 1/2 ](z6+1){1}12{ 26 }{ 13T2 }11312·1312·13
(z6+2){1}62{ 156 }{ 13T6 }113
(z6+3){1}32{ 78 }{ 13T5 }113
(z6+4){1}32{ 78 }{ 13T5 }113
(z6+5){1}22{ 52 }{ 13T4 }113
(z6+6){1}62{ 156 }{ 13T6 }113
(z6+7){1}62{ 156 }{ 13T6 }113
(z6+8){1}22{ 52 }{ 13T4 }113
(z6+9){1}32{ 78 }{ 13T5 }113
(z6+10){1}32{ 78 }{ 13T5 }113
(z6+11){1}62{ 156 }{ 13T6 }113
(z6+12){1}12{ 26 }{ 13T2 }113
7{(1,7), (13,0)}[ 7/12 ](z+1){1}112{ 156 }{ 13T6 }11312·1312·13
(z+2){1}112{ 156 }{ 13T6 }113
(z+3){1}112{ 156 }{ 13T6 }113
(z+4){1}112{ 156 }{ 13T6 }113
(z+5){1}112{ 156 }{ 13T6 }113
(z+6){1}112{ 156 }{ 13T6 }113
(z+7){1}112{ 156 }{ 13T6 }113
(z+8){1}112{ 156 }{ 13T6 }113
(z+9){1}112{ 156 }{ 13T6 }113
(z+10){1}112{ 156 }{ 13T6 }113
(z+11){1}112{ 156 }{ 13T6 }113
(z+12){1}112{ 156 }{ 13T6 }113
8{(1,8), (13,0)}[ 2/3 ](z4+1){1}23{ 78 }{ 13T5 }11312·1312·13
(z4+2){1}43{ 156 }{ 13T6 }113
(z4+3){1}23{ 78 }{ 13T5 }113
(z4+4){1}13{ 39 }{ 13T3 }113
(z4+5){1}43{ 156 }{ 13T6 }113
(z4+6){1}43{ 156 }{ 13T6 }113
(z4+7){1}43{ 156 }{ 13T6 }113
(z4+8){1}43{ 156 }{ 13T6 }113
(z4+9){1}23{ 78 }{ 13T5 }113
(z4+10){1}13{ 39 }{ 13T3 }113
(z4+11){1}43{ 156 }{ 13T6 }113
(z4+12){1}13{ 39 }{ 13T3 }113
9{(1,9), (13,0)}[ 3/4 ](z3+1){1}14{ 52 }{ 13T4 }11312·1312·13
(z3+2){1}34{ 156 }{ 13T6 }113
(z3+3){1}34{ 156 }{ 13T6 }113
(z3+4){1}34{ 156 }{ 13T6 }113
(z3+5){1}14{ 52 }{ 13T4 }113
(z3+6){1}34{ 156 }{ 13T6 }113
(z3+7){1}34{ 156 }{ 13T6 }113
(z3+8){1}14{ 52 }{ 13T4 }113
(z3+9){1}34{ 156 }{ 13T6 }113
(z3+10){1}34{ 156 }{ 13T6 }113
(z3+11){1}34{ 156 }{ 13T6 }113
(z3+12){1}14{ 52 }{ 13T4 }113
10{(1,10), (13,0)}[ 5/6 ](z2+1){1}16{ 78 }{ 13T5 }11312·1312·13
(z2+2){1}26{ 156 }{ 13T6 }113
(z2+3){1}16{ 78 }{ 13T5 }113
(z2+4){1}16{ 78 }{ 13T5 }113
(z2+5){1}26{ 156 }{ 13T6 }113
(z2+6){1}26{ 156 }{ 13T6 }113
(z2+7){1}26{ 156 }{ 13T6 }113
(z2+8){1}26{ 156 }{ 13T6 }113
(z2+9){1}16{ 78 }{ 13T5 }113
(z2+10){1}16{ 78 }{ 13T5 }113
(z2+11){1}26{ 156 }{ 13T6 }113
(z2+12){1}16{ 78 }{ 13T5 }113
11{(1,11), (13,0)}[ 11/12 ](z+1){1}112{ 156 }{ 13T6 }11312·1312·13
(z+2){1}112{ 156 }{ 13T6 }113
(z+3){1}112{ 156 }{ 13T6 }113
(z+4){1}112{ 156 }{ 13T6 }113
(z+5){1}112{ 156 }{ 13T6 }113
(z+6){1}112{ 156 }{ 13T6 }113
(z+7){1}112{ 156 }{ 13T6 }113
(z+8){1}112{ 156 }{ 13T6 }113
(z+9){1}112{ 156 }{ 13T6 }113
(z+10){1}112{ 156 }{ 13T6 }113
(z+11){1}112{ 156 }{ 13T6 }113
(z+12){1}112{ 156 }{ 13T6 }113
12{(1,12), (13,0)}[ 1 ](z12+1){1}21{ 26 }{ 13T2 }11312·1312·13
(z12+2){1}121{ 156 }{ 13T6 }113
(z12+3){1}61{ 78 }{ 13T5 }113
(z12+4){1}31{ 39 }{ 13T3 }113
(z12+5){1}41{ 52 }{ 13T4 }113
(z12+6){1}121{ 156 }{ 13T6 }113
(z12+7){1}121{ 156 }{ 13T6 }113
(z12+8){1}41{ 52 }{ 13T4 }113
(z12+9){1}61{ 78 }{ 13T5 }113
(z12+10){1}31{ 39 }{ 13T3 }113
(z12+11){1}121{ 156 }{ 13T6 }113
(z12+12){13}11{ 13 }{ 13T1 }1313
13{(1,13), (13,0)}[ 13/12 ](z+12){1}112{ 156 }{ 13T6 }13132132132