Low Degree Fields Unramified Outside of {∞, 67, 71}

Discriminant class: −71

∞ 67 71 a_{1} a_{2} a_{3} Over p = 67  Over p = 71  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 47 53
1. 1_{k} 0_{+} 1_{i} 0 71  2 0_{+} ∗ ∗ 1^{2} 1_{i} 71∗ 71∗  2 2 2 2
C_{2} 7  2  2  2  2 2

Discriminant class: −67

∞ 67 71 a_{1} a_{2} a_{3}  Over p = 67  Over p = 71 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 47 53
2. 1_{k} 1_{i} 0_{+} 0 67  1^{2} 1_{i} 67∗ 67∗  2 2 2 2 2 2
C_{2}  2  2 2  2

Discriminant class: 1

∞ 67 71 a_{1} a_{2} a_{3} Over p = 67 Over p = 71 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 47 53
3. 0_{+} 2_{+} 0_{+} -1 -22 -5 1^{3} 2_{+} 1  3 0_{+} 1  3  3 3 3 3 3
C_{3}  3 3 3 3 3  3

Discriminant class: 4757

∞ 67 71 a_{1}  a_{2} a_{3}  Over p = 67  Over p = 71  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 47 53
4. 0_{+} 1_{k} 1_{i} 0 -4757  1^{2} 1_{k} 67 67 1^{2} 1_{i} 71∗ 71∗ 2 2 2  2
C_{2} 5  2  2 2