Low Degree Fields Unramified Outside of {∞, 23, 67}

Discriminant class: −67

∞ 23 67 a_{1} a_{2} a_{3} Over p = 23  Over p = 67  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
1. 1_{k} 0_{+} 1_{i} 0 67  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 2
C_{2} 2 2 2 2

Discriminant class: −23

∞ 23 67 a_{1} a_{2} a_{3}  Over p = 23  Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
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 2 3 2 3 2

Discriminant class: 1

∞ 23 67 a_{1} a_{2} a_{3} Over p = 23 Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
4. 0_{+} 0_{+} 2_{+} -1 -22 -5 3 0_{+} 1  1^{3} 2_{+} 1  3  3 3 3 3 3
C_{3}  3 3 3 3  3

Discriminant class: 1541

∞ 23 67 a_{1}  a_{2} a_{3}  Over p = 23  Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
5. 0_{+} 1_{i} 1_{k} 0 -1541  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{k} 67 67 2 2  2 2 2
C_{2}  2 2 2