Low Degree Fields Ramifying Above {47, 61}

Discriminant class: −2867

∞ 47 61 a_{1} a_{2} a_{3}  Over p = 47  Over p = 61 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 2867  1^{2} 1_{i} 47∗ 47∗ 1^{2} 1_{+} 61 61 2  2 2  2 2 2
C_{2} 12  2 2  2 2
2. 1_{k} 1_{i} 1_{+} -1  2 20 1^{2} 1_{i} 47∗ 47∗ 1^{2} 1_{+} 61 61 2 3 2 2  2 2 2
S_{3}  3 3 3 2 2 3 2 2

Discriminant class: −47

∞ 47 61 a_{1} a_{2} a_{3}  Over p = 47  Over p = 61 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_{+} 0 -61 -244 1^{2} 1_{i} 47∗ 47∗ 1^{3} 2_{+} 1  3 2 3 2 2 3 2
S_{3} 12  2 2 2 3 2 2  3