Low Degree Fields Unramified Outside of {∞, 47, 73}

Discriminant class: −3431

∞ 47 73 a_{1} a_{2} a_{3}  Over p = 47  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 37 41 43 53 59
1. 1_{k} 1_{k} 1_{−} 0 3431  1^{2} 1_{k} 47 47 1^{2} 1_{−} 73∗ 73∗  2  2 2
C_{2} 66  2  2  2 2
2. 1_{k} 1_{k} 1_{−} -1 14 -16 1^{2} 1_{k} 47 47 1^{2} 1_{−} 73∗ 73∗  3 3 2  3 2 2
S_{3} 2  2 3  3 2 3 2 2

Discriminant class: −47

∞ 47 73 a_{1} a_{2} a_{3}  Over p = 47  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 37 41 43 53 59
3. 1_{k} 1_{i} 0_{+} 0 47  1^{2} 1_{i} 47∗ 47∗ 2 0_{+} ∗ ∗  2  2 2  2
C_{2} 5  2 2 2  2 2

Discriminant class: 1

∞ 47 73 a_{1} a_{2} a_{3} Over p = 47 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 37 41 43 53 59
4. 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

Discriminant class: 73

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