Low Degree Fields Unramified Outside of {∞, 31, 47}

Discriminant class: −47

∞ 31 47 a_{1} a_{2} a_{3} Over p = 31  Over p = 47  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 53 59 61
1. 1_{k} 0_{+} 1_{i} 0 47  2 0_{+} ∗ ∗ 1^{2} 1_{i} 47∗ 47∗  2  2 2  2
C_{2} 5  2 2  2 2

Discriminant class: −31

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

Discriminant class: 1

∞ 31 47 a_{1} a_{2} a_{3} Over p = 31 Over p = 47 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 53 59 61
4. 0_{+} 2_{+} 0_{+} 1 -10 -8 1^{3} 2_{+} 1  3 3 3 3 3 3 3
C_{3}  3 3 3 3 3

Discriminant class: 1457

∞ 31 47 a_{1}  a_{2} a_{3}  Over p = 31  Over p = 47  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 53 59 61
5. 0_{+} 1_{k} 1_{i} 0 -1457  1^{2} 1_{k} 31 31 1^{2} 1_{i} 47∗ 47∗  2 2  2 2
C_{2}  2 2  2  2