Low Degree Fields Unramified Outside of {∞, 31, 43}

Discriminant class: −43

∞ 31 43 a_{1} a_{2} a_{3} Over p = 31  Over p = 43  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 47 53 59 61
1. 1_{k} 0_{+} 1_{i} 0 43  1^{2} 1_{i} 43∗ 43∗ 2 2 2 2  2
C_{2}  2 2  2
2. 1_{k} 2_{+} 1_{i} -1 21 8 1^{3} 2_{+} 1  1^{2} 1_{i} 43∗ 43∗ 2 2 2 2 3  3 2
S_{3} 3  2 2 3 3 3  2

Discriminant class: −31

∞ 31 43 a_{1} a_{2} a_{3}  Over p = 31  Over p = 43 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 47 53 59 61
3. 1_{k} 1_{i} 0_{+} 0 31  1^{2} 1_{i} 31∗ 31∗ 2 0_{+} ∗ ∗  2  2 2 2
C_{2} 3  2 2 2  2  2
4. 1_{k} 1_{i} 0_{+} 0 1 -1 1^{2} 1_{i} 31∗ 31∗ 2 0_{+} ∗ ∗ 3 2 3 3 2 2 2 3
S_{3} 2 2 2 3 2 3 2

Discriminant class: 1

∞ 31 43 a_{1} a_{2} a_{3} Over p = 31 Over p = 43 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 47 53 59 61
5. 0_{+} 2_{+} 0_{+} 1 -10  -8 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3 3 3 3
C_{3}  3 3  3 3
6. 0_{+} 0_{+} 2_{+} -1 -14  -8 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3  3  3
7. 0_{+} 2_{+} 2_{+} -1 -444 3604 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3  3
C_{3} 12  3 3 3 3  3 3
8. 0_{+} 2_{+} 2_{+} 1 -444 1728 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3
C_{3} 3  3 3  3  3 3 3

Discriminant class: 1333

∞ 31 43 a_{1}  a_{2} a_{3}  Over p = 31  Over p = 43 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 47 53 59 61
9. 0_{+} 1_{i} 1_{k} 0 -1333  1^{2} 1_{i} 31∗ 31∗ 1^{2} 1_{k} 43 43 2  2 2 2 2 2 2
C_{2}  2  2