Low Degree Fields Ramifying Above {11, 71}

Discriminant class: −71

∞ 11 71 a_{1} a_{2} a_{3} Over p = 11  Over p = 71  2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
1. 1_{k} 2_{+} 1_{i} 0 11 -11 1^{3} 2_{+} ∗  1^{2} 1_{i} 71∗ 71∗ 3 3 3 2 2 2  2
S_{3} 2  3 2 3 2  2 2 2

Discriminant class: 781

∞ 11 71 a_{1} a_{2} a_{3}  Over p = 11  Over p = 71  2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
2. 0_{+} 1_{k} 1_{i} 0 -781  1^{2} 1_{k} 11 11 1^{2} 1_{i} 71∗ 71∗ 2  2 2
C_{2}  2 2  2 2 2 2