Low Degree Fields Unramified Outside of {∞, 23, 89}

Discriminant class: −2047

∞ 23 89 a_{1} a_{2} a_{3}  Over p = 23  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 29 31 37 41 43 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 2047  1^{2} 1_{k} 23 23 1^{2} 1_{−} 89∗ 89∗  2 2  2 2 2
C_{2} 18  2 2  2  2 2
2. 1_{k} 1_{k} 1_{−} 0  7 -5 1^{2} 1_{k} 23 23 1^{2} 1_{−} 89∗ 89∗ 3 2 2 3 2 2 2 3
S_{3} 2 2 3 2 3 2 2

Discriminant class: −23

∞ 23 89 a_{1} a_{2} a_{3}  Over p = 23  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 29 31 37 41 43 47 53 59
3. 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
4. 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 2 3 2

Discriminant class: 89

∞ 23 89 a_{1} a_{2} a_{3} Over p = 23  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 29 31 37 41 43 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