Low Degree Fields Unramified Outside of {∞, 2, 31}

Discriminant class: −62

∞ 2 31 a_{1} a_{2} a_{3} Over p = 2  Over p = 31  3 5 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} 3_{+} 1_{i} 0 62  1^{2} 3_{+} 2 2 1^{2} 1_{i} 31∗ 31∗  2  2 2 2
C_{2} 8  2

Discriminant class: −31

∞ 2 31 a_{1} a_{2} a_{3} Over p = 2  Over p = 31  3 5 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∗ 2 3 3 2 2 2 3 2
S_{3} 2 2 3 2 2 3 2

Discriminant class: −2

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

Discriminant class: −1

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

Discriminant class: 1

∞ 2 31 a_{1} a_{2} a_{3} Over p = 2  Over p = 31 3 5 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
6. 0_{+} 0_{+} 2_{+} 1 -10 -8  1^{3} 2_{+} 1  3 3 3 3 3 3 3
C_{3}  3 3 3  3 3

Discriminant class: 2

∞ 2 31 a_{1} a_{2} a_{3} Over p = 2  Over p = 31 3 5 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
7. 0_{+} 3_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2  2 2  2 2  2
C_{2}  2 2  2  2 2 2

Discriminant class: 31

∞ 2 31 a_{1} a_{2} a_{3}  Over p = 2  Over p = 31 3 5 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
8. 0_{+} 2_{i} 1_{k} 0 -31  1^{2} 2_{i} −1 −1 1^{2} 1_{k} 31 31  2  2 2 2
C_{2}  2 2  2 2 2 2

Discriminant class: 62

∞ 2 31 a_{1} a_{2} a_{3}  Over p = 2  Over p = 31 3 5 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
9. 0_{+} 3_{i} 1_{k} 0 -62  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 31 31 2 2 2 2  2
C_{2}  2 2