Low Degree Fields Unramified Outside of {∞, 3, 37}

Discriminant class: −111

∞ 3 37 a_{1} a_{2} a_{3} Over p = 3 Over p = 37 2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
1. 1_{k} 1_{i} 1_{+} 0 111  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 37 37  2 2  2
C_{2} 8  2 2 2 2 2  2
2. 1_{k} 3_{i} 1_{+} 0 3 -12 1^{3} 3_{i} 3∗  1^{2} 1_{+} 37 37  3 3 2 2 3 2 3
S_{3}  3 2 2 2 2 2 3 2
3. 1_{k} 5_{i} 1_{+} 0 9 -15 1^{3} 5_{i} 3∗ 1^{2} 1_{+} 37 37 3 3 2 2 2
S_{3}  3 2 2 2 2 2 3 2
4. 1_{k} 5_{i} 1_{+} 0 -9 -21 1^{3} 5_{i} 3∗  1^{2} 1_{+} 37 37 3 3  2 2 3 2 3
S_{3}  2 2 2 2 2  2
5. 1_{k} 5_{i} 1_{+} 0 27 -9 1^{3} 5_{i} 3∗  1^{2} 1_{+} 37 37 3 3 3 2 2 3 2 3
S_{3}  3 2 2 2 2 2 3 2

Discriminant class: −3

∞ 3 37 a_{1} a_{2} a_{3} Over p = 3 Over p = 37 2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
6. 1_{k} 1_{i} 0_{+} 1 1  1^{2} 1_{i} 3∗ 3∗  2 2  2  2  2
C_{2}  2  2  2 2 2
7. 1_{k} 5_{i} 0_{+} 0 0 -3 1^{3} 5_{i} 3∗  3 0_{+} 1  2 2 3 2 3 2 3 2
S_{3}  2 3 2 3 2 2 2
8. 1_{k} 1_{i} 2_{+} 0 0 -37 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} 1 2 2 3 2 3 2 2
S_{3} 3  2 3 2 3 2 2 2
9. 1_{k} 5_{i} 2_{+} 0 0 -111 1^{3} 5_{i} 3∗ 1^{3} 2_{+} 1 2 2 2 3 2 3 2
S_{3} 3  2 3 2 3 2 2 2
10. 1_{k} 5_{i} 2_{+} 0 0 -333 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2 3 2  2 3 2
S_{3} 3  2  2  2 2 2

Discriminant class: 1

∞ 3 37 a_{1} a_{2} a_{3} Over p = 3  Over p = 37 2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
11. 0_{+} 4_{+} 0_{+} 0 -3  1 1^{3} 4_{+} 1  3 3 3 3 3  3
C_{3}  3 3 3 3 3  3 3
12. 0_{+} 0_{+} 2_{+} 1 -12 11 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3  3 3 3
13. 0_{+} 4_{+} 2_{+} 0 -111 -37 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3  3 3 3 3 3
C_{3} 3  3 3 3 3 3 3
14. 0_{+} 4_{+} 2_{+} 0 -111 -370 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3  3 3 3
C_{3} 3  3 3  3 3 3 3 3

Discriminant class: 37

∞ 3 37 a_{1} a_{2} a_{3} Over p = 3  Over p = 37 2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
15. 0_{+} 0_{+} 1_{+} 0 -37  1^{2} 1_{+} 37 37 2 2  2 2 2 2
C_{2}  2 2  2  2 2