Low Degree Fields Ramifying Above {23, 47}

Discriminant class: −47

∞ 23 47 a_{1} a_{2} a_{3} Over p = 23  Over p = 47  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 53 59 61
1. 1_{k} 2_{+} 1_{i} -1 -38 109 1^{3} 2_{+} ∗  1^{2} 1_{i} 47∗ 47∗ 3 3 2 3 2 2  2
S_{3}  2 2  2 2  3

Discriminant class: 1081

∞ 23 47 a_{1}  a_{2} a_{3}  Over p = 23  Over p = 47  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 53 59 61
2. 0_{+} 1_{k} 1_{i} 0 -1081  1^{2} 1_{k} 23 23 1^{2} 1_{i} 47∗ 47∗  2  2 2
C_{2}  2 2 2 2  2  2