Low Degree Fields Unramified Outside of {∞, 71, 73}

Discriminant class: −5183

∞ 71 73 a_{1} a_{2} a_{3}  Over p = 71  Over p = 73 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 37 41 43 47 53
1. 1_{k} 1_{i} 1_{+} 0 5183  1^{2} 1_{i} 71∗ 71∗ 1^{2} 1_{+} 73 73  2
C_{2} 80  2 2  2 2

Discriminant class: −71

∞ 71 73 a_{1} a_{2} a_{3}  Over p = 71  Over p = 73 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 37 41 43 47 53
2. 1_{k} 1_{i} 0_{+} 0 71  1^{2} 1_{i} 71∗ 71∗  2 2 2 2
C_{2} 7  2  2  2  2 2
3. 1_{k} 1_{i} 2_{+} -1 -24 -119 1^{2} 1_{i} 71∗ 71∗ 1^{3} 2_{+} 1  3 3 3 2 2 2 2 3
S_{3} 3  2 3 2 3 2 3 2 2

Discriminant class: 1

∞ 71 73 a_{1} a_{2} a_{3} Over p = 71 Over p = 73 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 37 41 43 47 53
4. 0_{+} 0_{+} 2_{+} -1 -24 27 3 0_{+} 1  1^{3} 2_{+} 1  3  3  3 3  3
C_{3}  3 3 3 3 3  3 3

Discriminant class: 73

∞ 71 73 a_{1} a_{2} a_{3} Over p = 71  Over p = 73 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 37 41 43 47 53
5. 0_{+} 0_{+} 1_{+} 0 -73  1^{2} 1_{+} 73 73  2 2 2 2 2
C_{2}  2 2  2 2 2