Low Degree Fields Unramified Outside of {∞, 37, 71}

Discriminant class: −2627

∞ 37 71 a_{1} a_{2} a_{3}  Over p = 37  Over p = 71  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 2627  1^{2} 1_{+} 37 37 1^{2} 1_{i} 71∗ 71∗ 2  2 2 2  2
C_{2} 12  2  2 2 2 2
2. 1_{k} 1_{+} 1_{i} -1  9 -2 1^{2} 1_{+} 37 37 1^{2} 1_{i} 71∗ 71∗ 2 3 2 2 2  3 2
S_{3}  3 2 3 2 2 2 2

Discriminant class: −71

∞ 37 71 a_{1} a_{2} a_{3} Over p = 37  Over p = 71  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 71  1^{2} 1_{i} 71∗ 71∗  2 2 2 2
C_{2} 7  2  2 2  2 2 2
4. 1_{k} 2_{+} 1_{i} 0 -37 -148 1^{3} 2_{+} 1  1^{2} 1_{i} 71∗ 71∗  3 3 2 2 2 2 3
S_{3} 3  2  2 2 3 2 2 2

Discriminant class: 1

∞ 37 71 a_{1} a_{2} a_{3} Over p = 37 Over p = 71 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

Discriminant class: 37

∞ 37 71 a_{1} a_{2} a_{3} Over p = 37 Over p = 71 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
6. 0_{+} 1_{+} 0_{+} 0 -37  1^{2} 1_{+} 37 37  2  2  2 2 2
C_{2}  2 2 2  2  2