Low Degree Fields Ramifying Above {11, 19, 23}

Discriminant class: −4807

∞ 11 19 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 19  Over p = 23  2 3 5 7 13 17 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} 1_{k} 1_{i} 1_{i} 0 4807  1^{2} 1_{k} 11 11 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗  2 2  2
C_{2} 40  2

Discriminant class: 253

∞ 11 19 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 19  Over p = 23  2 3 5 7 13 17 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_{k} 2_{+} 1_{i} -1 -63 -164 1^{2} 1_{k} 11 11 1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 2 3 2 3 2 3 2 3
S_{3} 3  2 2 3 3 2  3 2