Low Degree Fields Unramified Outside of {∞, 19, 37}

Discriminant class: −703

∞ 19 37 a_{1} a_{2} a_{3}  Over p = 19  Over p = 37  2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 41 43 47 53 59 61
1. 1_{k} 1_{k} 1_{−} 0 703  1^{2} 1_{k} 19 19 1^{2} 1_{−} 37∗ 37∗  2 2  2 2
C_{2} 14  2 2  2  2

Discriminant class: −19

∞ 19 37 a_{1} a_{2} a_{3}  Over p = 19  Over p = 37 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
2. 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

Discriminant class: 1

∞ 19 37 a_{1} a_{2} a_{3} Over p = 19 Over p = 37 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
3. 0_{+} 2_{+} 0_{+} -1 -6  7 1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3  3 3 3 3 3 3
4. 0_{+} 0_{+} 2_{+} 1 -12 11 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3  3 3
C_{3}  3  3 3 3
5. 0_{+} 2_{+} 2_{+} 1 -234 -729 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3  3 3 3
C_{3} 12  3  3 3  3 3
6. 0_{+} 2_{+} 2_{+} -1 -234 1432 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3
C_{3} 3  3  3 3 3 3

Discriminant class: 37

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