Low Degree Fields Ramifying Above {43, 67}

Discriminant class: −43

∞ 43 67 a_{1} a_{2} a_{3}  Over p = 43  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 31 37 41 47 53 59
1. 1_{k} 1_{i} 2_{+} 0 -134 -603 1^{2} 1_{i} 43∗ 43∗ 1^{3} 2_{+} 1  2 2 2 2 3 3 3 2
S_{3} 6 2 3 2 3

Discriminant class: 1

∞ 43 67 a_{1} a_{2}  a_{3} Over p = 43 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 31 37 41 47 53 59
2. 0_{+} 2_{+} 2_{+} -1 -960 6829 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3  3
C_{3} 3  3 3  3 3 3 3
3. 0_{+} 2_{+} 2_{+} -1 -960 -10457 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3} 12  3  3 3 3

Discriminant class: 2881

∞ 43 67 a_{1}  a_{2} a_{3}  Over p = 43  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 31 37 41 47 53 59
4. 0_{+} 1_{k} 1_{i} 0 -2881  1^{2} 1_{k} 43 43 1^{2} 1_{i} 67∗ 67∗  2 2  2
C_{2}  2 2 2 2  2