Low Degree Fields Unramified Outside of {∞, 37, 43}

Discriminant class: −1591

∞ 37 43 a_{1} a_{2} a_{3}  Over p = 37  Over p = 43 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 47 53 59 61
1. 1_{k} 1_{−} 1_{k} 0 1591  1^{2} 1_{−} 37∗ 37∗ 1^{2} 1_{k} 43 43  2  2  2 2
C_{2} 22  2  2  2

Discriminant class: −43

∞ 37 43 a_{1} a_{2} a_{3} Over p = 37  Over p = 43  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 47 53 59 61
2. 1_{k} 0_{+} 1_{i} 0 43  2 0_{+} ∗ ∗ 1^{2} 1_{i} 43∗ 43∗ 2 2 2 2  2
C_{2}  2  2

Discriminant class: 1

∞ 37 43 a_{1} a_{2}  a_{3} Over p = 37 Over p = 43 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 47 53 59 61
3. 0_{+} 2_{+} 0_{+} 1 -12  11 1^{3} 2_{+} 1  3 3 3 3  3 3 3
C_{3}  3  3 3 3
4. 0_{+} 0_{+} 2_{+} -1 -14  -8 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3  3  3
5. 0_{+} 2_{+} 2_{+} -1 -530 -4007 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3
C_{3} 3  3 3 3 3  3
6. 0_{+} 2_{+} 2_{+} 1 -530 825 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3  3
C_{3} 3  3 3 3 3  3 3 3

Discriminant class: 37

∞ 37 43 a_{1} a_{2} a_{3} Over p = 37 Over p = 43 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 47 53 59 61
7. 0_{+} 1_{+} 0_{+} 0 -37  1^{2} 1_{+} 37 37 2 0_{+} ∗ ∗ 2  2  2 2 2
C_{2}  2 2 2  2 2