Low Degree Fields Unramified Outside of {∞, 37, 47}

Discriminant class: −1739

∞ 37 47 a_{1} a_{2} a_{3}  Over p = 37  Over p = 47  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 53 59 61
1. 1_{k} 1_{+} 1_{i} 0 1739  1^{2} 1_{+} 37 37 1^{2} 1_{i} 47∗ 47∗ 2  2  2
C_{2} 20  2  2 2

Discriminant class: −47

∞ 37 47 a_{1} a_{2} a_{3} Over p = 37  Over p = 47  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 53 59 61
2. 1_{k} 0_{+} 1_{i} 0 47  1^{2} 1_{i} 47∗ 47∗  2  2 2  2
C_{2} 5  2 2 2 2 2
3. 1_{k} 2_{+} 1_{i} 0 -37 -259 1^{3} 2_{+} 1  1^{2} 1_{i} 47∗ 47∗ 3 3 2  2 2 3 2
S_{3} 3  2 2 2 2 2  3

Discriminant class: 1

∞ 37 47 a_{1} a_{2} a_{3} Over p = 37 Over p = 47 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 53 59 61
4. 0_{+} 2_{+} 0_{+} 1 -12 11 1^{3} 2_{+} 1  3 3 3 3  3 3 3
C_{3}  3  3 3 3

Discriminant class: 37

∞ 37 47 a_{1} a_{2} a_{3} Over p = 37 Over p = 47 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 53 59 61
5. 0_{+} 1_{+} 0_{+} 0 -37  1^{2} 1_{+} 37 37  2  2  2 2 2
C_{2}  2 2 2  2  2 2