Low Degree Fields Unramified Outside of {∞, 17, 47}

Discriminant class: −799

∞ 17 47 a_{1} a_{2} a_{3}  Over p = 17  Over p = 47  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 53 59 61
1. 1_{k} 1_{+} 1_{i} 0 799  1^{2} 1_{+} 17 17 1^{2} 1_{i} 47∗ 47∗  2  2  2 2
C_{2} 16  2  2  2

Discriminant class: −47

∞ 17 47 a_{1} a_{2} a_{3} Over p = 17  Over p = 47  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 53 59 61
2. 1_{k} 0_{+} 1_{i} 0 47  1^{2} 1_{i} 47∗ 47∗  2  2 2 2 2
C_{2} 5  2 2  2 2

Discriminant class: 17

∞ 17 47 a_{1} a_{2} a_{3} Over p = 17 Over p = 47 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 53 59 61
3. 0_{+} 1_{+} 0_{+} 1 -4  1^{2} 1_{+} 17 17  2 2 2 2  2
C_{2}  2 2 2 2  2