Low Degree Fields Unramified Outside of {∞, 31, 37}

Discriminant class: −1147

∞ 31 37 a_{1} a_{2} a_{3}  Over p = 31  Over p = 37  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 41 43 47 53 59 61
1. 1_{k} 1_{k} 1_{−} 0 1147  1^{2} 1_{k} 31 31 1^{2} 1_{−} 37∗ 37∗ 2 2 2  2  2
C_{2} 6  2 2
2. 1_{k} 1_{k} 1_{−} -1 -3 8 1^{2} 1_{k} 31 31 1^{2} 1_{−} 37∗ 37∗ 2 2 2 3 2 3 2
S_{3}  3 3 3 3 3 2 2 3

Discriminant class: −31

∞ 31 37 a_{1} a_{2} a_{3}  Over p = 31  Over p = 37 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 41 43 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 3 2 2 3 2

Discriminant class: 1

∞ 31 37 a_{1} a_{2} a_{3} Over p = 31 Over p = 37 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 41 43 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 -12 11  1^{3} 2_{+} 1  3 3 3 3  3 3 3
C_{3}  3  3 3 3
7. 0_{+} 2_{+} 2_{+} -1 -382 2209 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3  3 3 3
C_{3} 12  3 3  3 3
8. 0_{+} 2_{+} 2_{+} 1 -382 85 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3  3
C_{3} 3  3  3  3

Discriminant class: 37

∞ 31 37 a_{1} a_{2} a_{3} Over p = 31  Over p = 37 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 41 43 47 53 59 61
9. 0_{+} 0_{+} 1_{+} 0 -37  2 0_{+} ∗ ∗ 1^{2} 1_{+} 37 37 2  2  2 2 2
C_{2}  2 2  2  2 2