Low Degree Fields Unramified Outside of {∞, 47, 97}

Discriminant class: −4559

∞ 47 97 a_{1} a_{2} a_{3}  Over p = 47  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 53 59
1. 1_{k} 1_{i} 1_{+} 0 4559  1^{2} 1_{i} 47∗ 47∗ 1^{2} 1_{+} 97 97  2 2  2
C_{2} 72  2 2  2  2
2. 1_{k} 1_{i} 1_{+} 0  -1 -13 1^{2} 1_{i} 47∗ 47∗ 1^{2} 1_{+} 97 97 3 3 3 2 2  2
S_{3}  3 3 2 2 3 2 3 2

Discriminant class: −47

∞ 47 97 a_{1} a_{2} a_{3}  Over p = 47  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 53 59
3. 1_{k} 1_{i} 0_{+} 0 47  1^{2} 1_{i} 47∗ 47∗  2  2 2  2
C_{2} 5  2 2 2  2 2
4. 1_{k} 1_{i} 2_{+} -1 162 -891 1^{2} 1_{i} 47∗ 47∗ 1^{3} 2_{+} 1  3  2 3 2 2 3 2
S_{3} 6  2 2 2 3 2 2 3 3

Discriminant class: 1

∞ 47 97 a_{1} a_{2} a_{3} Over p = 47 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 53 59
5. 0_{+} 0_{+} 2_{+} -1 -32 79 1^{3} 2_{+} 1 3 3 3 3 3 3 3
C_{3}  3 3 3 3 3 3 3 3

Discriminant class: 97

∞ 47 97 a_{1} a_{2} a_{3} Over p = 47  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 53 59
6. 0_{+} 0_{+} 1_{+} 0 -97  1^{2} 1_{+} 97 97  2 2  2 2 2
C_{2}  2 2  2 2  2