Low Degree Fields Ramifying Above {47, 97}

Discriminant class: −4559

∞ 47 97 a_{1} a_{2} a_{3}  Over p = 47  Over p = 97 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 53 59
1. 1_{k} 1_{i} 1_{+} 0 4559  1^{2} 1_{i} 47∗ 47∗ 1^{2} 1_{+} 97 97  2 2  2
C_{2} 72  2 2  2  2
2. 1_{k} 1_{i} 1_{+} 0  -1 -13 1^{2} 1_{i} 47∗ 47∗ 1^{2} 1_{+} 97 97 3 3 3 2 2  2
S_{3}  3 3 2 2 3 2 3 2

Discriminant class: −47

∞ 47 97 a_{1} a_{2} a_{3}  Over p = 47  Over p = 97 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 53 59
3. 1_{k} 1_{i} 2_{+} -1 162 -891 1^{2} 1_{i} 47∗ 47∗ 1^{3} 2_{+} 1  3  2 3 2 2 3 2
S_{3} 6  2 2 2 3 2 2 3 3