Low Degree Fields Unramified Outside of {∞, 23, 37}

Discriminant class: −851

∞ 23 37 a_{1} a_{2} a_{3}  Over p = 23  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 29 31 41 43 47 53 59 61
1. 1_{k} 1_{k} 1_{−} 0 851  1^{2} 1_{k} 23 23 1^{2} 1_{−} 37∗ 37∗ 2  2 2 2
C_{2} 10  2 2  2 2

Discriminant class: −23

∞ 23 37 a_{1} a_{2} a_{3}  Over p = 23  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 29 31 41 43 47 53 59 61
2. 1_{k} 1_{i} 0_{+} 0 23  1^{2} 1_{i} 23∗ 23∗ 2 0_{+} ∗ ∗  2 2 2  2 2
C_{2} 3  2  2  2
3. 1_{k} 1_{i} 0_{+} -1 0 1 1^{2} 1_{i} 23∗ 23∗ 2 0_{+} ∗ ∗ 3 3 2 2 2 3 2 2
S_{3} 3 3 3 2 3 2 2

Discriminant class: 1

∞ 23 37 a_{1} a_{2} a_{3} Over p = 23 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 29 31 41 43 47 53 59 61
4. 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: 37

∞ 23 37 a_{1} a_{2} a_{3} Over p = 23  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 29 31 41 43 47 53 59 61
5. 0_{+} 0_{+} 1_{+} 0 -37  2 0_{+} ∗ ∗ 1^{2} 1_{+} 37 37 2  2  2 2 2
C_{2}  2 2  2  2 2