Low Degree Fields Unramified Outside of {∞, 47, 67}

Discriminant class: −67

∞ 47 67 a_{1} a_{2} a_{3} Over p = 47  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 41 43 53 59
1. 1_{k} 0_{+} 1_{i} 0 67  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 2
C_{2} 2 2 2 2

Discriminant class: −47

∞ 47 67 a_{1} a_{2} a_{3}  Over p = 47  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 41 43 53 59
2. 1_{k} 1_{i} 0_{+} 0 47  1^{2} 1_{i} 47∗ 47∗ 2 0_{+} ∗ ∗  2  2 2  2
C_{2} 5  2 2 2  2 2

Discriminant class: 1

∞ 47 67 a_{1} a_{2} a_{3} Over p = 47 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 41 43 53 59
3. 0_{+} 0_{+} 2_{+} -1 -22 -5 3 0_{+} 1 1^{3} 2_{+} 1 3 3 3 3 3 3
C_{3}  3 3 3 3 3

Discriminant class: 3149

∞ 47 67 a_{1}  a_{2} a_{3}  Over p = 47  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 41 43 53 59
4. 0_{+} 1_{i} 1_{k} 0 -3149  1^{2} 1_{i} 47∗ 47∗ 1^{2} 1_{k} 67 67 2 2  2  2
C_{2}  2 2  2