Low Degree Fields Ramifying Above {41, 67}

Discriminant class: −2747

∞ 41 67 a_{1} a_{2} a_{3}  Over p = 41  Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 43 47 53 59
1. 1_{k} 1_{−} 1_{k} 0 2747  1^{2} 1_{−} 41∗ 41∗ 1^{2} 1_{k} 67 67 2  2  2 2
C_{2} 18  2 2  2 2
2. 1_{k} 1_{−} 1_{k} -1  1 30 1^{2} 1_{−} 41∗ 41∗ 1^{2} 1_{k} 67 67 2  2 3 3 3 2 2
S_{3}  3 2 2 3 2 2 3 3

Discriminant class: −67

∞ 41 67 a_{1} a_{2} a_{3} Over p = 41  Over p = 67  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 43 47 53 59
3. 1_{k} 2_{+} 1_{i} 0 -41 -164 1^{3} 2_{+} ∗  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 2  3
S_{3}  3  2 3 2 3 2