Low Degree Fields Ramifying Above {43, 71}

Discriminant class: −71

∞ 43 71 a_{1} a_{2} a_{3} Over p = 43  Over p = 71  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} 2_{+} 1_{i} 0 -43 -129 1^{3} 2_{+} 1  1^{2} 1_{i} 71∗ 71∗ 3  3 2 2 2 2
S_{3} 6  2  2 3 2 2 2 2

Discriminant class: −43

∞ 43 71 a_{1} a_{2} a_{3}  Over p = 43  Over p = 71 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. 1_{k} 1_{i} 2_{+} 0 -71 -426 1^{2} 1_{i} 43∗ 43∗ 1^{3} 2_{+} ∗  2 2 2 2 3 3  2
S_{3} 5  3 2  2  3  3

Discriminant class: 3053

∞ 43 71 a_{1}  a_{2} a_{3}  Over p = 43  Over p = 71 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
3. 0_{+} 1_{i} 1_{k} 0 -3053  1^{2} 1_{i} 43∗ 43∗ 1^{2} 1_{k} 71 71 2 2 2  2 2 2 2
C_{2}  2 2 2 2 2 2 2 2