Low Degree Fields Unramified Outside of {∞, 23, 43}

Discriminant class: −43

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

Discriminant class: −23

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

Discriminant class: 1

∞ 23 43 a_{1} a_{2} a_{3} Over p = 23 Over p = 43 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 47 53 59 61
4. 0_{+} 0_{+} 2_{+} -1 -14 -8 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3  3  3

Discriminant class: 989

∞ 23 43 a_{1} a_{2} a_{3}  Over p = 23  Over p = 43 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 47 53 59 61
5. 0_{+} 1_{i} 1_{k} 0 -989  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{k} 43 43 2 2  2  2
C_{2}  2  2