Low Degree Fields Unramified Outside of {∞, 71, 97}

Discriminant class: −6887

∞ 71 97 a_{1} a_{2} a_{3}  Over p = 71  Over p = 97  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_{k} 1_{−} 0 6887  1^{2} 1_{k} 71 71 1^{2} 1_{−} 97∗ 97∗  2  2  2
C_{2} 78  2 2 2  2 2
2. 1_{k} 1_{k} 1_{−} -1  4 -17 1^{2} 1_{k} 71 71 1^{2} 1_{−} 97∗ 97∗ 3 3 2 3 2  2
S_{3}  2 2 2 3 3 2 2

Discriminant class: −71

∞ 71 97 a_{1} a_{2} a_{3}  Over p = 71  Over p = 97 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
3. 1_{k} 1_{i} 0_{+} 0 71  1^{2} 1_{i} 71∗ 71∗ 2 0_{+} ∗ ∗  2 2 2 2
C_{2} 7  2  2  2  2 2

Discriminant class: 1

∞ 71 97 a_{1} a_{2} a_{3} Over p = 71 Over p = 97 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 -32 79 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3 3
C_{3}  3 3 3 3 3 3  3

Discriminant class: 97

∞ 71 97 a_{1} a_{2} a_{3} Over p = 71  Over p = 97 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 -97  2 0_{+} ∗ ∗ 1^{2} 1_{+} 97 97  2 2  2 2 2
C_{2}  2 2  2 2