Low Degree Fields Unramified Outside of {∞, 19, 61}

Discriminant class: −1159

∞ 19 61 a_{1} a_{2} a_{3}  Over p = 19  Over p = 61 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_{i} 1_{+} 0 1159  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{+} 61 61  2  2 2 2 2 2
C_{2} 16  2 2

Discriminant class: −19

∞ 19 61 a_{1} a_{2} a_{3}  Over p = 19  Over p = 61 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
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 -81 314 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} 1  2 2 3 3 3 2 3 3
S_{3} 3  2 2 2 2 3 3 2 2

Discriminant class: 1

∞ 19 61 a_{1} a_{2}  a_{3} Over p = 19 Over p = 61 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
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 -20  9 3 0_{+} 1  1^{3} 2_{+} 1  3  3 3  3 3
C_{3}  3 3  3 3  3
6. 0_{+} 2_{+} 2_{+} -1 -386 -1760 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3  3 3 3
C_{3} 3  3  3  3
7. 0_{+} 2_{+} 2_{+} -1 -386 1717 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3  3
C_{3} 3  3 3  3 3 3 3 3

Discriminant class: 61

∞ 19 61 a_{1} a_{2} a_{3} Over p = 19  Over p = 61 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
8. 0_{+} 0_{+} 1_{+} 0 -61  1^{2} 1_{+} 61 61 2  2 2  2 2
C_{2}  2 2 2  2  2 2