Low Degree Fields Unramified Outside of {∞, 2, 89}

Discriminant class: −178

∞ 2 89 a_{1} a_{2} a_{3}  Over p = 2  Over p = 89 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 1_{k} 3_{i} 1_{+} 0 178  1^{2} 3_{i} −2 −2 1^{2} 1_{+} 89 89 2 2  2
C_{2} 8  2 2 2 2 2

Discriminant class: −89

∞ 2 89 a_{1} a_{2} a_{3}  Over p = 2  Over p = 89 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 1_{k} 2_{i} 1_{+} 0 89  1^{2} 2_{i} −1 −1 1^{2} 1_{+} 89 89  2 2
C_{2} 12  2  2 2  2
3. 1_{k} 2_{i} 1_{+} -1 1 7 1^{2} 2_{i} −1 −1 1^{2} 1_{+} 89 89 3 3  2 2 3 3 3
S_{3}  2 3 2 2 3 2 3

Discriminant class: −2

∞ 2 89 a_{1} a_{2} a_{3}  Over p = 2  Over p = 89 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
4. 1_{k} 3_{i} 0_{+} 0 2  1^{2} 3_{i} −2 −2  2 2  2  2
C_{2}  2 2 2  2 2

Discriminant class: −1

∞ 2 89 a_{1} a_{2} a_{3}  Over p = 2  Over p = 89 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
5. 1_{k} 2_{i} 0_{+} 0 1  1^{2} 2_{i} −1 −1  2  2 2  2 2
C_{2}  2  2 2  2

Discriminant class: 2

∞ 2 89 a_{1} a_{2} a_{3} Over p = 2  Over p = 89 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
6. 0_{+} 3_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2  2 2  2 2  2
C_{2}  2  2  2  2 2

Discriminant class: 89

∞ 2 89 a_{1} a_{2} a_{3} Over p = 2  Over p = 89 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
7. 0_{+} 0_{+} 1_{+} 0 -89  1^{2} 1_{+} 89 89 2  2  2  2 2
C_{2}  2 2 2 2 2  2

Discriminant class: 178

∞ 2 89 a_{1} a_{2} a_{3} Over p = 2  Over p = 89 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
8. 0_{+} 3_{+} 1_{+} 0 -178  1^{2} 3_{+} 2 2 1^{2} 1_{+} 89 89  2 2 2  2
C_{2} 2  2  2  2