Low Degree Fields Ramifying Above {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 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
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 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

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} 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
7. 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
8. 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
9. 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
10. 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