Low Degree Fields Unramified Outside of {∞, 67, 73}

Discriminant class: −4891

∞ 67 73 a_{1} a_{2} a_{3}  Over p = 67  Over p = 73 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} 1_{i} 1_{+} 0 4891  1^{2} 1_{i} 67∗ 67∗ 1^{2} 1_{+} 73 73 2 2  2
C_{2} 20  2  2  2

Discriminant class: −67

∞ 67 73 a_{1} a_{2} a_{3}  Over p = 67  Over p = 73 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
3. 1_{k} 1_{i} 2_{+} -1 -97 538 1^{2} 1_{i} 67∗ 67∗ 1^{3} 2_{+} 1  2 2 2 2 2 2  3
S_{3} 3  3  2 3 2 2  2

Discriminant class: 1

∞ 67 73 a_{1} a_{2} a_{3} Over p = 67 Over p = 73 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_{+} 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
5. 0_{+} 0_{+} 2_{+} -1 -24  27 3 0_{+} 1  1^{3} 2_{+} 1  3  3  3 3  3
C_{3}  3 3 3 3 3  3 3
6. 0_{+} 2_{+} 2_{+} 1 -1630 18296 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3
C_{3} 3  3 3 3 3  3
7. 0_{+} 2_{+} 2_{+} -1 -1630 25723 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3 3 3 3
C_{3} 3  3  3 3

Discriminant class: 73

∞ 67 73 a_{1} a_{2} a_{3} Over p = 67  Over p = 73 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
8. 0_{+} 0_{+} 1_{+} 0 -73  1^{2} 1_{+} 73 73  2 2 2 2 2
C_{2}  2 2  2 2 2