Low Degree Fields Unramified Outside of {∞, 37, 67}

Discriminant class: −2479

∞ 37 67 a_{1} a_{2} a_{3}  Over p = 37  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 41 43 47 53 59
1. 1_{k} 1_{+} 1_{i} 0 2479  1^{2} 1_{+} 37 37 1^{2} 1_{i} 67∗ 67∗  2  2 2  2 2
C_{2} 24  2 2  2  2 2
2. 1_{k} 1_{+} 1_{i} 0 -11 -17 1^{2} 1_{+} 37 37 1^{2} 1_{i} 67∗ 67∗ 3 2 3 2 2 3 2 2
S_{3} 2 2 2 3 3 2 2

Discriminant class: −67

∞ 37 67 a_{1} a_{2} a_{3} Over p = 37  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 41 43 47 53 59
3. 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
4. 1_{k} 2_{+} 1_{i} -1 25 26 1^{3} 2_{+} 1  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 2  3
S_{3} 24  3  2 2 2  2 3

Discriminant class: 1

∞ 37 67 a_{1} a_{2}  a_{3} Over p = 37 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 41 43 47 53 59
5. 0_{+} 2_{+} 0_{+} 1 -12  11 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3  3 3 3
C_{3}  3  3 3
6. 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
7. 0_{+} 2_{+} 2_{+} 1 -826 -1469 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3  3
C_{3} 3  3 3 3 3  3 3 3
8. 0_{+} 2_{+} 2_{+} 1 -826 5968 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3  3
C_{3} 3  3 3 3  3 3 3

Discriminant class: 37

∞ 37 67 a_{1} a_{2} a_{3} Over p = 37 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 41 43 47 53 59
9. 0_{+} 1_{+} 0_{+} 0 -37  1^{2} 1_{+} 37 37  2  2  2 2 2
C_{2}  2 2 2  2  2