Low Degree Fields Unramified Outside of {∞, 73, 79}

Discriminant class: −5767

∞ 73 79 a_{1} a_{2} a_{3}  Over p = 73  Over p = 79  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
1. 1_{k} 1_{+} 1_{i} 0 5767  1^{2} 1_{+} 73 73 1^{2} 1_{i} 79∗ 79∗  2 2  2 2
C_{2} 36  2 2 2
2. 1_{k} 1_{+} 1_{i} -1 12 -45 1^{2} 1_{+} 73 73 1^{2} 1_{i} 79∗ 79∗ 3 2 2 3 2 2  3
S_{3}  3 2 2 2 3 3 3

Discriminant class: −79

∞ 73 79 a_{1} a_{2} a_{3} Over p = 73  Over p = 79  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
3. 1_{k} 0_{+} 1_{i} 0 79  1^{2} 1_{i} 79∗ 79∗  2  2  2
C_{2} 5  2  2 2 2 2 2
4. 1_{k} 2_{+} 1_{i} 0 73 -438 1^{3} 2_{+} 1  1^{2} 1_{i} 79∗ 79∗  2 3 2 3  2
S_{3} 3  3 2 3 2 2 2 2 2

Discriminant class: 1

∞ 73 79 a_{1} a_{2} a_{3} Over p = 73 Over p = 79 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
5. 0_{+} 2_{+} 0_{+} -1 -24  27 1^{3} 2_{+} 1  3 0_{+} 1  3  3  3 3  3
C_{3}  3 3 3 3 3  3 3
6. 0_{+} 0_{+} 2_{+} 1 -26  41 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3  3
C_{3}  3 3 3 3  3 3 3
7. 0_{+} 2_{+} 2_{+} 1 -1922 -22000 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3  3
C_{3} 12  3 3 3 3 3  3
8. 0_{+} 2_{+} 2_{+} 1 -1922 -4699 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3
C_{3} 3  3  3 3 3

Discriminant class: 73

∞ 73 79 a_{1} a_{2} a_{3} Over p = 73 Over p = 79 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
9. 0_{+} 1_{+} 0_{+} 0 -73  1^{2} 1_{+} 73 73  2 2 2 2 2
C_{2}  2 2  2 2 2
10. 0_{+} 1_{+} 2_{+} 0 -79 -237 1^{2} 1_{+} 73 73 1^{3} 2_{+} 1  3  2 2 2 2 2 3
S_{3} 3  3 2 2 3 3 2 2 2