Low Degree Fields Ramifying Above {19, 23, 29}

Discriminant class: −667

∞ 19 23 29 a_{1} a_{2} a_{3} Over p = 19  Over p = 23  Over p = 29 2 3 5 7 11 13 17 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_{i} 1_{+} -1 -63 710 1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2 2  3 3 2
S_{3} 3  3 2 3 2 2 3 3 2

Discriminant class: 12673

∞ 19 23 29 a_{1}  a_{2} a_{3}  Over p = 19  Over p = 23  Over p = 29  2 3 5 7 11 13 17 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_{i} 1_{−} 0 -12673  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{−} 29∗ 29∗  2 2  2
C_{2} 2  2  2  2