Low Degree Fields Unramified Outside of {∞, 3, 19}

Discriminant class: −19

∞ 3 19 a_{1} a_{2} a_{3} Over p = 3  Over p = 19  2 5 7 11 13 17 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
1. 1_{k} 0_{+} 1_{i} -1 5  2 0_{+} ∗ ∗ 1^{2} 1_{i} 19∗ 19∗ 2  2  2
C_{2}  2 2 2  2 2
2. 1_{k} 4_{+} 1_{i} 0 6 -5 1^{3} 4_{+} ∗  1^{2} 1_{i} 19∗ 19∗ 2  3 3 2 3 3 2
S_{3}  2 2 2 3 3 2 2 3

Discriminant class: −3

∞ 3 19 a_{1} a_{2} a_{3} Over p = 3 Over p = 19 2 5 7 11 13 17 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 1_{k} 1_{i} 0_{+} 1 1  1^{2} 1_{i} 3∗ 3∗  2 2  2  2 2 2
C_{2}  2  2 2 2
4. 1_{k} 5_{i} 0_{+} 0 0 -3 1^{3} 5_{i} 3∗  3 0_{+} 1  2 2 3 2 3 2 2 2
S_{3}  3 3 2 3 2 2 2
5. 1_{k} 1_{i} 2_{+} -1 -6 -12 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} 1  2 2 3 2 3 2 2 2
S_{3} 3  3 3 2 3 2 2 2 3
6. 1_{k} 5_{i} 2_{+} 0 0 -171 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2 3 2 3 2 2 2
S_{3} 6  2  2 2 2 3
7. 1_{k} 5_{i} 2_{+} 0 0 -57 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2  2  2 2 2
S_{3} 6  3 3 2 3 2 2 2 3

Discriminant class: 1

∞ 3 19 a_{1} a_{2} a_{3} Over p = 3  Over p = 19 2 5 7 11 13 17 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
8. 0_{+} 4_{+} 0_{+} 0 -3 1 1^{3} 4_{+} 1  3 3 3 3 3  3 3
C_{3}  3  3 3 3  3 3
9. 0_{+} 0_{+} 2_{+} -1 -6 7 3 0_{+} 1  1^{3} 2_{+} 1  3 3  3 3 3 3
C_{3}  3 3 3 3 3 3
10. 0_{+} 4_{+} 2_{+} 0 -57 19 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3  3 3 3 3 3
C_{3} 3  3  3  3
11. 0_{+} 4_{+} 2_{+} 0 -57 152 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3 3  3  3
C_{3} 3  3  3  3 3 3 3

Discriminant class: 57

∞ 3 19 a_{1} a_{2} a_{3} Over p = 3  Over p = 19  2 5 7 11 13 17 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
12. 0_{+} 1_{k} 1_{i} 0 -57  1^{2} 1_{k} 3 3 1^{2} 1_{i} 19∗ 19∗  2  2 2 2 2
C_{2}  2 2  2