Low Degree Fields Unramified Outside of {∞, 2, 37}

Discriminant class: −74

∞ 2 37 a_{1} a_{2} a_{3}  Over p = 2  Over p = 37  3 5 7 11 13 17 19 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} 3_{k} 1_{−} 0 74  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 37∗ 37∗  2  2 2
C_{2} 10  2 2 2 2

Discriminant class: −37

∞ 2 37 a_{1} a_{2} a_{3}  Over p = 2  Over p = 37 3 5 7 11 13 17 19 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} 2_{i} 1_{+} 0 37  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 37 37 2 2 2 2 2 2
C_{2} 2 2 2 2

Discriminant class: −2

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

Discriminant class: −1

∞ 2 37 a_{1} a_{2} a_{3}  Over p = 2  Over p = 37 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
4. 1_{k} 2_{i} 0_{+} 0 1  1^{2} 2_{i} −1 −1  2  2 2  2 2
C_{2}  2  2 2  2
5. 1_{k} 2_{i} 2_{+} -1 -12 26 1^{2} 2_{i} −1 −1 1^{3} 2_{+} 1  2 3 2 2  3 2 2
S_{3} 6  3 2 3 2 2  2 3

Discriminant class: 1

∞ 2 37 a_{1} a_{2} a_{3} Over p = 2  Over p = 37 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
6. 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

Discriminant class: 2

∞ 2 37 a_{1} a_{2} a_{3} Over p = 2  Over p = 37 3 5 7 11 13 17 19 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_{+} 3_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗ 2 2  2 2  2
C_{2}  2  2  2 2 2

Discriminant class: 37

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

Discriminant class: 74

∞ 2 37 a_{1} a_{2} a_{3}  Over p = 2  Over p = 37  3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 41 43 47 53 59 61
10. 0_{+} 3_{−} 1_{−} 0 -74  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 37∗ 37∗ 2  2  2  2
C_{2} 2  2  2