Low Degree Fields Ramifying Above {19, 71}

Discriminant class: −71

∞ 19 71 a_{1} a_{2} a_{3} Over p = 19  Over p = 71  2 3 5 7 11 13 17 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} -1 -6 64 1^{3} 2_{+} 1  1^{2} 1_{i} 71∗ 71∗  3 3 2 2 2 2 2
S_{3} 3  2 3 2 3 2 2 2

Discriminant class: −19

∞ 19 71 a_{1} a_{2} a_{3}  Over p = 19  Over p = 71 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 1_{k} 1_{i} 2_{+} -1 -47 234 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2 3 3  2  3
S_{3} 11  2 2 2 2 3  2 2

Discriminant class: 1349

∞ 19 71 a_{1}  a_{2} a_{3}  Over p = 19  Over p = 71 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
3. 0_{+} 1_{i} 1_{k} 0 -1349  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{k} 71 71 2 2  2 2  2 2
C_{2}  2  2  2