Low Degree Fields Unramified Outside of {∞, 19, 43}

Discriminant class: −43

∞ 19 43 a_{1} a_{2} a_{3} Over p = 19  Over p = 43  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 47 53 59 61
1. 1_{k} 0_{+} 1_{i} 0 43  2 0_{+} ∗ ∗ 1^{2} 1_{i} 43∗ 43∗ 2 2 2 2
C_{2} 2 2 2

Discriminant class: −19

∞ 19 43 a_{1} a_{2} a_{3}  Over p = 19  Over p = 43 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 47 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
3. 1_{k} 1_{i} 2_{+} -1 29 -180 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} 1  2 2  3 3 2 3 3
S_{3} 3  2 2 2 2  2 2 3

Discriminant class: 1

∞ 19 43 a_{1} a_{2} a_{3} Over p = 19 Over p = 43 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 47 53 59 61
4. 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
5. 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
6. 0_{+} 2_{+} 2_{+} -1 -272 121 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3  3
C_{3} 3  3 3 3 3 3  3 3
7. 0_{+} 2_{+} 2_{+} -1 -272 1755 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3  3 3
C_{3} 3  3 3 3 3 3 3

Discriminant class: 817

∞ 19 43 a_{1} a_{2} a_{3}  Over p = 19  Over p = 43  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 47 53 59 61
8. 0_{+} 1_{k} 1_{i} 0 -817  1^{2} 1_{k} 19 19 1^{2} 1_{i} 43∗ 43∗  2 2  2
C_{2} 5  2  2  2 2 2