Low Degree Fields Unramified Outside of {∞, 19, 47}

Discriminant class: −47

∞ 19 47 a_{1} a_{2} a_{3} Over p = 19  Over p = 47  2 3 5 7 11 13 17 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} 0_{+} 1_{i} 0 47  2 0_{+} ∗ ∗ 1^{2} 1_{i} 47∗ 47∗  2  2 2  2
C_{2} 5  2 2  2 2

Discriminant class: −19

∞ 19 47 a_{1} a_{2} a_{3}  Over p = 19  Over p = 47 2 3 5 7 11 13 17 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} 1_{i} 0_{+} -1 5  1^{2} 1_{i} 19∗ 19∗  2 2  2
C_{2}  2 2 2 2  2 2

Discriminant class: 1

∞ 19 47 a_{1} a_{2} a_{3} Over p = 19 Over p = 47 2 3 5 7 11 13 17 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_{+} 2_{+} 0_{+} -1 -6 7 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3  3 3 3
C_{3}  3  3 3 3 3 3

Discriminant class: 893

∞ 19 47 a_{1} a_{2} a_{3}  Over p = 19  Over p = 47  2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 53 59 61
4. 0_{+} 1_{k} 1_{i} 0 -893  1^{2} 1_{k} 19 19 1^{2} 1_{i} 47∗ 47∗ 2 2 2  2  2
C_{2}  2  2 2 2