Low Degree Fields Unramified Outside of {∞, 43, 47}

Discriminant class: −47

∞ 43 47 a_{1} a_{2} a_{3} Over p = 43  Over p = 47  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 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: −43

∞ 43 47 a_{1} a_{2} a_{3}  Over p = 43  Over p = 47 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 53 59 61
2. 1_{k} 1_{i} 0_{+} 0 43  1^{2} 1_{i} 43∗ 43∗  2 2 2 2  2
C_{2}  2  2  2

Discriminant class: 1

∞ 43 47 a_{1} a_{2} a_{3} Over p = 43 Over p = 47 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 53 59 61
3. 0_{+} 2_{+} 0_{+} -1 -14 -8 1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3 3  3  3

Discriminant class: 2021

∞ 43 47 a_{1}  a_{2} a_{3}  Over p = 43  Over p = 47  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 53 59 61
4. 0_{+} 1_{k} 1_{i} 0 -2021  1^{2} 1_{k} 43 43 1^{2} 1_{i} 47∗ 47∗ 2 2  2 2 2
C_{2} 3  2  2 2 2  2
5. 0_{+} 1_{k} 1_{i} 0  -8 -1 1^{2} 1_{k} 43 43 1^{2} 1_{i} 47∗ 47∗ 2 2 3 2 2 2 3 3
S_{3}  2 3 2 2 2 3 3 2