Low Degree Fields Unramified Outside of {∞, 37, 73}

Discriminant class: 1

∞ 37 73 a_{1} a_{2} a_{3} Over p = 37 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 31 41 43 47 53 59
1. 0_{+} 2_{+} 0_{+} 1 -12 11 1^{3} 2_{+} 1  3 3 3 3  3 3 3
C_{3}  3  3 3
2. 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
3. 0_{+} 2_{+} 2_{+} 1 -900 -100 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3 3 3
C_{3} 3  3 3 3  3
4. 0_{+} 2_{+} 2_{+} -1 -900 8203 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3  3
C_{3} 3  3 3 3 3  3 3 3

Discriminant class: 37

∞ 37 73 a_{1} a_{2} a_{3} Over p = 37 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 31 41 43 47 53 59
5. 0_{+} 1_{+} 0_{+} 0 -37  1^{2} 1_{+} 37 37  2  2  2 2 2
C_{2}  2 2 2  2  2
6. 0_{+} 1_{+} 2_{+} -1 -97 392 1^{2} 1_{+} 37 37 1^{3} 2_{+} 1  2 3 2  3 2 2 2
S_{3} 3  2 2 2  2 3 3 2

Discriminant class: 73

∞ 37 73 a_{1} a_{2} a_{3} Over p = 37  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 31 41 43 47 53 59
7. 0_{+} 0_{+} 1_{+} 0 -73  1^{2} 1_{+} 73 73  2 2 2 2 2
C_{2}  2 2  2 2 2 2

Discriminant class: 2701

∞ 37 73 a_{1} a_{2} a_{3} Over p = 37 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 31 41 43 47 53 59
8. 0_{+} 1_{+} 1_{+} 0 -2701  1^{2} 1_{+} 37 37 1^{2} 1_{+} 73 73 2  2 2  2
C_{2} 2  2  2 2