Low Degree Fields Unramified Outside of {∞, 73, 89}

Discriminant class: 1

∞ 73 89 a_{1} a_{2} a_{3} Over p = 73 Over p = 89 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. 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

Discriminant class: 73

∞ 73 89 a_{1} a_{2} a_{3} Over p = 73 Over p = 89 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
2. 0_{+} 1_{+} 0_{+} 0 -73  1^{2} 1_{+} 73 73  2 2 2 2 2
C_{2}  2 2  2 2 2

Discriminant class: 89

∞ 73 89 a_{1} a_{2} a_{3} Over p = 73  Over p = 89 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. 0_{+} 0_{+} 1_{+} 0 -89 1^{2} 1_{+} 89 89 2 2 2 2
C_{2}  2 2 2 2 2 2

Discriminant class: 6497

∞ 73 89 a_{1} a_{2} a_{3} Over p = 73 Over p = 89 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
4. 0_{+} 1_{+} 1_{+} 0 -6497  1^{2} 1_{+} 73 73 1^{2} 1_{+} 89 89  2 2  2  2 2
C_{2} 4  2  2 2  2 2