Low Degree Fields Ramifying Above {13, 19, 23}

Discriminant class: −299

∞ 13 19 23 a_{1} a_{2} a_{3}  Over p = 13  Over p = 19  Over p = 23  2 3 5 7 11 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_{+} 2_{+} 1_{i} -1 -44 292 1^{2} 1_{+} 13 13 1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 2 3 3 3 3 2 3 2
S_{3} 6  3 2 2 2 2 2 2 3

Discriminant class: 5681

∞ 13 19 23 a_{1}  a_{2} a_{3}  Over p = 13  Over p = 19  Over p = 23  2 3 5 7 11 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_{−} 1_{i} 1_{i} 0 -5681  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗  2  2 2
C_{2} 2  2  2 2  2 2