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 T9 T10 T11 T12 T17 T19 T21 T22 T27 T28 T33 T40 T41 T42 T43 Total {2,3} ℚ(√-3) 1 5 1 2 3 12 txt gp {2,3} ℚ(√-1) 1 5 2 6 14 txt gp {2,3} ℚ(√2) 1 2 3 1 4 7 18 31 67 txt gp {2,3} ℚ(√-2) 1 5 5 41 52 txt gp {2,3} ℚ(√3) 1 1 4 4 6 41 57 txt gp {2,3} ℚ(√-6) 1 1 4 2 2 10 txt gp {2,3} ℚ(√6) 1 1 4 3 4 61 74 txt gp {2,5} ℚ(√-1) 1 1 3 19 2 5 3 14 11 6 35 22 161 4 57 222 566 txt gp {2,5} ℚ(√5) 1 4 10 9 4 14 5 10 8 9 28 4 33 43 37 51 159 429 txt gp {3,7} ℚ(√-3) 0 {3,7} ℚ(√-7) 0 {3,7} ℚ(√21) 0 {3,11} ℚ(√-3) 1 2 3 txt gp {3,11} ℚ(√-11) 1 2 3 txt gp {3,11} ℚ(√33) 1 2 3 txt gp {7,11} ℚ(√-7) 1 1 2 1 5 txt gp {7,11} ℚ(√-11) 1 1 1 3 txt gp