Tables of Decics Containing a Quadratic Subfield



Cases where S contains one prime

S T1 T2 T4 T10 Total    
{2}         0    
{3}         0    
{5} 1   2 2 5 txt gp
{7}         0    
{11} 1       1 txt gp
{13}         0    
{17}         0    
{19}         0    
{23}         0    
{29}         0    
{31} 1       1 txt gp
{37}         0    
{41} 1       1 txt gp
{43}         0    
{47}   1     1 txt gp



Cases where S contains two primes

The following table also includes an entry for the quadratic subfield K. Each data set is complete in the sense that it contains every field having K as a subfield.

S K T1 T2 T3 T4 T5 T6 T11 T12 T22 T28 T40 T41 T42 T43 Total    
{2,3}         1       5   1 2   3 12 txt gp
{2,3}         1       5     2   6 14 txt gp
{2,3}       1       2 3 1 4 7 18 31 67 txt gp
{2,3}         1       5     5   41 52 txt gp
{2,3}         1     1 4   4 6   41 57 txt gp
{2,3}         1     1 4     2   2 10 txt gp
{2,3}         1     1 4   3 4   61 74 txt gp
{3,7}                             0    
{3,7}                             0    
{3,7}                             0    
{3,11} 1           2               3 txt gp
{3,11} 1           2               3 txt gp
{3,11} 1           2               3 txt gp
{7,11} 1 1       2     1           5 txt gp
{7,11} 1   1           1           3 txt gp


The next table is only guaranteed to contain all the fields whose discriminant has an exponent of 2 which is less than or equal to 24.

S K T1 T2 T3 T5 T6 T11 T12 T17 T19 T21 T22 T27 T33 T40 T41 T43 Total    
{2,5} 1 1 3 19 2 5 3 14 8 6 35 15 41 4 46 82 285 txt gp