Low Degree Fields Ramifying Above {5, 7, 19}

Discriminant class: 133

∞ 5 7 19 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 19 2 3 11 13 17 23 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. 0_{+} 2_{+} 1_{i} 1_{k} 0 -10 -5 1^{3} 2_{+} ∗ 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 19 19 2 3 3 3 2 2 3
S_{3}  2 3 3 2 2 3 2 2

Discriminant class: 665

∞ 5 7 19 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 19 2 3 11 13 17 23 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_{k} 1_{k} 0 -665  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 1^{2} 1_{k} 19 19  2  2  2 2
C_{2} 2  2  2