Low Degree Fields Unramified Outside of {∞, 17, 89}

Discriminant class: 17

∞ 17 89 a_{1} a_{2} a_{3} Over p = 17 Over p = 89 2 3 5 7 11 13 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 0_{+} 1_{+} 0_{+} 1 -4 1^{2} 1_{+} 17 17 2 2 2 2 2
C_{2}  2 2 2 2

Discriminant class: 89

∞ 17 89 a_{1} a_{2} a_{3} Over p = 17  Over p = 89 2 3 5 7 11 13 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 0_{+} 0_{+} 1_{+} 0 -89  1^{2} 1_{+} 89 89  2  2  2 2 2
C_{2}  2 2 2 2 2  2

Discriminant class: 1513

∞ 17 89 a_{1} a_{2} a_{3} Over p = 17 Over p = 89 2 3 5 7 11 13 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
3. 0_{+} 1_{+} 1_{+} 0 -1513  1^{2} 1_{+} 17 17 1^{2} 1_{+} 89 89  2  2 2 2
C_{2} 2  2  2