Low Degree Fields Unramified Outside of {∞, 19, 89}

Discriminant class: −1691

∞ 19 89 a_{1} a_{2} a_{3}  Over p = 19  Over p = 89  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 43 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 1691  1^{2} 1_{k} 19 19 1^{2} 1_{−} 89∗ 89∗ 2  2  2
C_{2} 18  2  2
2. 1_{k} 1_{k} 1_{−} -1  1 -24 1^{2} 1_{k} 19 19 1^{2} 1_{−} 89∗ 89∗ 2  3 2 3 3 3 2
S_{3}  3 3 3 3 2  2 3

Discriminant class: −19

∞ 19 89 a_{1} a_{2} a_{3}  Over p = 19  Over p = 89 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 43 47 53 59
3. 1_{k} 1_{i} 0_{+} -1 5  1^{2} 1_{i} 19∗ 19∗ 2 0_{+} ∗ ∗ 2 2  2
C_{2}  2 2 2 2  2 2
4. 1_{k} 1_{i} 2_{+} 0 -89 -356 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2 3 3 3 2 3 3
S_{3} 2  2 2 2 2 3 3 2 2

Discriminant class: 1

∞ 19 89 a_{1} a_{2} a_{3} Over p = 19 Over p = 89 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 43 47 53 59
5. 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

Discriminant class: 89

∞ 19 89 a_{1} a_{2} a_{3} Over p = 19  Over p = 89 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 43 47 53 59
6. 0_{+} 0_{+} 1_{+} 0 -89  2 0_{+} ∗ ∗ 1^{2} 1_{+} 89 89  2  2  2  2
C_{2}  2 2 2 2 2  2