Low Degree Fields Unramified Outside of {∞, 43, 97}

Discriminant class: −4171

∞ 43 97 a_{1} a_{2} a_{3}  Over p = 43  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 47 53 59
1. 1_{k} 1_{i} 1_{+} 0 4171  1^{2} 1_{i} 43∗ 43∗ 1^{2} 1_{+} 97 97 2 2  2 2
C_{2} 16  2  2  2

Discriminant class: −43

∞ 43 97 a_{1} a_{2} a_{3}  Over p = 43  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 47 53 59
2. 1_{k} 1_{i} 0_{+} 0 43  1^{2} 1_{i} 43∗ 43∗  2 2 2 2  2
C_{2}  2  2
3. 1_{k} 1_{i} 2_{+} -1 65 -600 1^{2} 1_{i} 43∗ 43∗ 1^{3} 2_{+} 1  2 2 2 2 3 3 3 2
S_{3} 18 2 3 2 3 3

Discriminant class: 1

∞ 43 97 a_{1} a_{2} a_{3} Over p = 43 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 47 53 59
4. 0_{+} 2_{+} 0_{+} -1 -14  -8 1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3 3  3
5. 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
6. 0_{+} 2_{+} 2_{+} 1 -1390 -8033 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3  3 3
C_{3} 3  3 3 3  3 3
7. 0_{+} 2_{+} 2_{+} -1 -1390 16375 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3  3
C_{3} 3  3 3  3  3

Discriminant class: 97

∞ 43 97 a_{1} a_{2} a_{3} Over p = 43  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 47 53 59
8. 0_{+} 0_{+} 1_{+} 0 -97  1^{2} 1_{+} 97 97  2 2  2 2 2
C_{2}  2 2  2 2  2