Low Degree Fields Ramifying Above {31, 67}

Discriminant class: 1

∞ 31 67 a_{1} a_{2}  a_{3} Over p = 31 Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 37 41 43 47 53 59
1. 0_{+} 2_{+} 2_{+} 1 -692 5231 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3  3
C_{3} 3  3 3  3 3 3 3
2. 0_{+} 2_{+} 2_{+} 1 -692 -7231 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3  3 3
C_{3} 12  3 3 3 3 3 3 3 3

Discriminant class: 2077

∞ 31 67 a_{1}  a_{2} a_{3}  Over p = 31  Over p = 67  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 37 41 43 47 53 59
3. 0_{+} 1_{k} 1_{i} 0 -2077  1^{2} 1_{k} 31 31 1^{2} 1_{i} 67∗ 67∗ 2  2 2  2
C_{2}  2 2 2 2