Low Degree Fields Unramified Outside of {∞, 31, 73}

Discriminant class: −2263

∞ 31 73 a_{1} a_{2} a_{3}  Over p = 31  Over p = 73  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 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 2263  1^{2} 1_{k} 31 31 1^{2} 1_{−} 73∗ 73∗  2 2 2
C_{2} 22  2  2  2  2

Discriminant class: −31

∞ 31 73 a_{1} a_{2} a_{3}  Over p = 31  Over p = 73 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 47 53 59
2. 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
3. 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 2 3

Discriminant class: 1

∞ 31 73 a_{1} a_{2}  a_{3} Over p = 31 Over p = 73 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 47 53 59
4. 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 3
5. 0_{+} 0_{+} 2_{+} -1 -24  27 3 0_{+} 1  1^{3} 2_{+} 1  3  3  3 3  3
C_{3}  3 3 3 3  3 3 3
6. 0_{+} 2_{+} 2_{+} -1 -754 -7711 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3  3 3
C_{3} 21  3 3 3  3 3 3
7. 0_{+} 2_{+} 2_{+} -1 -754 5867 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3  3 3
C_{3} 3  3 3  3 3 3  3

Discriminant class: 73

∞ 31 73 a_{1} a_{2} a_{3} Over p = 31  Over p = 73 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 47 53 59
8. 0_{+} 0_{+} 1_{+} 0 -73  2 0_{+} ∗ ∗ 1^{2} 1_{+} 73 73  2 2 2 2 2
C_{2}  2  2 2 2 2