Low Degree Fields Unramified Outside of {∞, 5, 31}

Discriminant class: −155

∞ 5 31 a_{1} a_{2} a_{3} Over p = 5  Over p = 31  2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 37 41 43 47 53 59 61
1. 1_{k} 1_{+} 1_{i} 0 155  1^{2} 1_{+} 5 5 1^{2} 1_{i} 31∗ 31∗ 2  2 2
C_{2} 4  2  2  2

Discriminant class: −31

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

Discriminant class: 1

∞ 5 31 a_{1} a_{2} a_{3} Over p = 5  Over p = 31 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 37 41 43 47 53 59 61
4. 0_{+} 0_{+} 2_{+} 1 -10 -8 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3
C_{3}  3 3 3  3 3

Discriminant class: 5

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