Low Degree Fields Ramifying Above {59, 71}

Discriminant class: −71

∞ 59 71 a_{1} a_{2} a_{3} Over p = 59  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 47 53
1. 1_{k} 2_{+} 1_{i} -1 20 83 1^{3} 2_{+} ∗  1^{2} 1_{i} 71∗ 71∗ 3 3 3 2 2 2 2 3
S_{3}  2 3 2 3 2 3 2 2

Discriminant class: 4189

∞ 59 71 a_{1}  a_{2} a_{3}  Over p = 59  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 47 53
2. 0_{+} 1_{k} 1_{i} 0 -4189  1^{2} 1_{k} 59 59 1^{2} 1_{i} 71∗ 71∗ 2  2  2
C_{2}  2 2 2  2