Low Degree Fields Unramified Outside of {∞, 47, 89}

Discriminant class: −4183

∞ 47 89 a_{1} a_{2} a_{3}  Over p = 47  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 53 59
1. 1_{k} 1_{i} 1_{+} 0 4183  1^{2} 1_{i} 47∗ 47∗ 1^{2} 1_{+} 89 89  2 2 2 2
C_{2} 28  2  2

Discriminant class: −47

∞ 47 89 a_{1} a_{2} a_{3}  Over p = 47  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 53 59
2. 1_{k} 1_{i} 0_{+} 0 47  1^{2} 1_{i} 47∗ 47∗  2  2 2  2
C_{2} 5  2 2 2  2 2

Discriminant class: 89

∞ 47 89 a_{1} a_{2} a_{3} Over p = 47  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 53 59
3. 0_{+} 0_{+} 1_{+} 0 -89  1^{2} 1_{+} 89 89  2  2  2  2
C_{2}  2 2 2 2 2 2  2