Low Degree Fields Ramifying Above {5, 67}

Discriminant class: −335

∞ 5 67 a_{1} a_{2} a_{3} Over p = 5 Over p = 67 2 3 7 11 13 17 19 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} 1_{−} 1_{k} 0 335  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 67 67  2  2  2
C_{2} 18  2 2 2  2
2. 1_{k} 1_{−} 1_{k} -1 4 1 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 67 67 3 3 3 2  2  2
S_{3}  3 2 2 2 3 2 3 3

Discriminant class: −67

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