Low Degree Fields Unramified Outside of {∞, 31, 97}

Discriminant class: −3007

∞ 31 97 a_{1} a_{2} a_{3}  Over p = 31  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 37 41 43 47 53 59
1. 1_{k} 1_{i} 1_{+} 0 3007  1^{2} 1_{i} 31∗ 31∗ 1^{2} 1_{+} 97 97  2 2 2 2  2
C_{2} 20  2 2  2 2

Discriminant class: −31

∞ 31 97 a_{1} a_{2} a_{3}  Over p = 31  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 37 41 43 47 53 59
2. 1_{k} 1_{i} 0_{+} 0 31  1^{2} 1_{i} 31∗ 31∗  2  2 2 2
C_{2} 3  2 2 2  2  2
3. 1_{k} 1_{i} 0_{+} 0 1 -1 1^{2} 1_{i} 31∗ 31∗ 3 0_{+} 1  3 2 3 3 2 2 2 3
S_{3} 2 2 2 3 2 2 3
4. 1_{k} 1_{i} 2_{+} -1 -32 -309 1^{2} 1_{i} 31∗ 31∗ 1^{3} 2_{+} 1  3 2 3 3 2 2 2 3
S_{3} 3  2 2 2  2 3 2 3
5. 1_{k} 1_{i} 2_{+} -1 -32 -115 1^{2} 1_{i} 31∗ 31∗ 1^{3} 2_{+} 1  3 2  2 2 2 3
S_{3} 3  2 2 2 3 2 3 2
6. 1_{k} 1_{i} 2_{+} 0 97 -194 1^{2} 1_{i} 31∗ 31∗ 1^{3} 2_{+} 1  2 3 3 2 2 2
S_{3} 15  2 2 2 3 2 3 2 3

Discriminant class: 1

∞ 31 97 a_{1}  a_{2} a_{3} Over p = 31 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 37 41 43 47 53 59
7. 0_{+} 2_{+} 0_{+} 1 -10  -8 1^{3} 2_{+} 1  3 3 3 3 3 3 3
C_{3}  3 3 3  3 3
8. 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
9. 0_{+} 2_{+} 2_{+} 1 -1002 6905 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3  3
C_{3} 3  3 3 3  3  3
10. 0_{+} 2_{+} 2_{+} -1 -1002 -891 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3  3 3 3
C_{3} 3  3 3  3  3

Discriminant class: 97

∞ 31 97 a_{1} a_{2} a_{3} Over p = 31  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 37 41 43 47 53 59
11. 0_{+} 0_{+} 1_{+} 0 -97  1^{2} 1_{+} 97 97  2 2  2 2 2
C_{2}  2 2 2 2  2
12. 0_{+} 2_{+} 1_{+} 0 -31 -31 1^{3} 2_{+} 1  1^{2} 1_{+} 97 97 3 3 2 2 3 2 2 2
S_{3} 3  2 2 2 2  3  2