Low Degree Fields Unramified Outside of {∞, 29, 37}

Discriminant class: 1

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

Discriminant class: 29

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

Discriminant class: 37

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

Discriminant class: 1073

∞ 29 37 a_{1}  a_{2} a_{3}  Over p = 29  Over p = 37  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d  s 23 31 41 43 47 53 59 61
4. 0_{+} 1_{−} 1_{−} 0 -1073  1^{2} 1_{−} 29∗ 29∗ 1^{2} 1_{−} 37∗ 37∗  2 2  2 2
C_{2} 2  2  2  2  2