Low Degree Fields Ramifying Above {53, 67}

Discriminant class: −3551

∞ 53 67 a_{1} a_{2} a_{3}  Over p = 53  Over p = 67 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 59
1. 1_{k} 1_{−} 1_{k} 0 3551  1^{2} 1_{−} 53∗ 53∗ 1^{2} 1_{k} 67 67  2 2 2  2
C_{2} 58  2  2

Discriminant class: −67

∞ 53 67 a_{1} a_{2} a_{3} Over p = 53  Over p = 67  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 59
2. 1_{k} 2_{+} 1_{i} -1 -35 -744 1^{3} 2_{+} ∗  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 2 3
S_{3} 4  3 3 2 3 2 2 3