Low Degree Fields Ramifying Above {19, 67}

Discriminant class: −67

∞ 19 67 a_{1} a_{2} a_{3} Over p = 19  Over p = 67  2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
1. 1_{k} 2_{+} 1_{i} 0 -38 -95 1^{3} 2_{+} 1  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 2 3 3
S_{3} 3  2 3 2 2 3 2 3

Discriminant class: 1

∞ 19 67 a_{1} a_{2}  a_{3} Over p = 19 Over p = 67 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 0_{+} 2_{+} 2_{+} 1 -424 -2876 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3  3
C_{3} 3  3 3 3 3  3 3
3. 0_{+} 2_{+} 2_{+} 1 -424 943 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3  3
C_{3} 3  3 3 3  3 3 3 3

Discriminant class: 1273

∞ 19 67 a_{1}  a_{2} a_{3}  Over p = 19  Over p = 67 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
4. 0_{+} 1_{i} 1_{k} 0 -1273  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{k} 67 67  2 2 2
C_{2}  2  2  2  2