Low Degree Fields Ramifying Above {47, 71}

Discriminant class: −71

∞ 47 71 a_{1} a_{2} a_{3} Over p = 47  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 43 53 59
1. 1_{k} 2_{+} 1_{i} -1 16 604 1^{3} 2_{+} ∗  1^{2} 1_{i} 71∗ 71∗  3  2 2 2 2 3
S_{3} 20  2 3 2 3 2 3 2 2

Discriminant class: 3337

∞ 47 71 a_{1}  a_{2} a_{3}  Over p = 47  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 43 53 59
2. 0_{+} 1_{k} 1_{i} 0 -3337  1^{2} 1_{k} 47 47 1^{2} 1_{i} 71∗ 71∗  2 2  2 2
C_{2}  2  2 2 2