Low Degree Fields Unramified Outside of {∞, 43, 89}

Discriminant class: −3827

∞ 43 89 a_{1} a_{2} a_{3}  Over p = 43  Over p = 89  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 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 3827  1^{2} 1_{k} 43 43 1^{2} 1_{−} 89∗ 89∗ 2  2  2
C_{2} 22  2  2  2  2

Discriminant class: −43

∞ 43 89 a_{1} a_{2} a_{3}  Over p = 43  Over p = 89 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 47 53 59
2. 1_{k} 1_{i} 0_{+} 0 43  1^{2} 1_{i} 43∗ 43∗ 2 0_{+} ∗ ∗ 2 2 2 2  2
C_{2}  2  2
3. 1_{k} 1_{i} 2_{+} 1 119 300 1^{2} 1_{i} 43∗ 43∗ 1^{3} 2_{+} ∗  2 2 2 2  3 3 2
S_{3}  3 2 3 2 3 3 3 3

Discriminant class: 1

∞ 43 89 a_{1} a_{2} a_{3} Over p = 43 Over p = 89 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 47 53 59
4. 0_{+} 2_{+} 0_{+} -1 -14 -8 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3 3  3

Discriminant class: 89

∞ 43 89 a_{1} a_{2} a_{3} Over p = 43  Over p = 89 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 47 53 59
5. 0_{+} 0_{+} 1_{+} 0 -89  2 0_{+} ∗ ∗ 1^{2} 1_{+} 89 89  2  2  2  2
C_{2}  2 2 2 2 2  2