Low Degree Fields Ramifying Above {37, 71}

Discriminant class: −2627

∞ 37 71 a_{1} a_{2} a_{3}  Over p = 37  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 41 43 47 53 59
1. 1_{k} 1_{+} 1_{i} 0 2627  1^{2} 1_{+} 37 37 1^{2} 1_{i} 71∗ 71∗ 2  2 2 2  2
C_{2} 12  2  2 2 2 2
2. 1_{k} 1_{+} 1_{i} -1  9 -2 1^{2} 1_{+} 37 37 1^{2} 1_{i} 71∗ 71∗ 2 3 2 2 2  3 2
S_{3}  3 2 3 2 2 2 2

Discriminant class: −71

∞ 37 71 a_{1} a_{2} a_{3} Over p = 37  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 41 43 47 53 59
3. 1_{k} 2_{+} 1_{i} 0 -37 -148 1^{3} 2_{+} 1  1^{2} 1_{i} 71∗ 71∗  3 3 2 2 2 2 3
S_{3} 3  2  2 2 3 2 2 2