Low Degree Fields Ramifying Above {7, 13, 23}

Discriminant class: −299

∞ 7 13 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 23  2 3 5 11 17 19 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
1. 1_{k} 2_{+} 1_{+} 1_{i} -1 5 -118 1^{3} 2_{+} 1  1^{2} 1_{+} 13 13 1^{2} 1_{i} 23∗ 23∗ 2 3  3 2 3 3 2
S_{3} 3  2 2 2 2 2 2 3

Discriminant class: 2093

∞ 7 13 23 a_{1}  a_{2} a_{3}  Over p = 7  Over p = 13  Over p = 23  2 3 5 11 17 19 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
2. 0_{+} 1_{i} 1_{−} 1_{i} 0 -2093  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{i} 23∗ 23∗ 2 2 2  2
C_{2} 2  2  2