Low Degree Fields Unramified Outside of {∞, 3, 67}

Discriminant class: −67

∞ 3 67 a_{1} a_{2} a_{3} Over p = 3  Over p = 67  2 5 7 11 13 17 19 23
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  2 0_{+} ∗ ∗ 1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2
C_{2} 2 2 2 2
2. 1_{k} 4_{+} 1_{i} 0 6 -13 1^{3} 4_{+} ∗  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 3 3 3
S_{3} 2 2 2 2 3

Discriminant class: −3

∞ 3 67 a_{1} a_{2} a_{3} Over p = 3 Over p = 67 2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
3. 1_{k} 1_{i} 0_{+} 1 1  1^{2} 1_{i} 3∗ 3∗  2 2  2  2  2
C_{2}  2  2  2 2 2
4. 1_{k} 5_{i} 0_{+} 0 0 -3 1^{3} 5_{i} 3∗  2 2 3 2 3 2 3 2
S_{3}  2 3 3 2 3 2 2 2
5. 1_{k} 3_{i} 2_{+} 0 0 -67 1^{3} 3_{i} 3∗ 1^{3} 2_{+} 1 2 2 3 2 3 2 3 2
S_{3} 6  2 3 3 2 3 2 2 2
6. 1_{k} 5_{i} 2_{+} 0 0 -603 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2  2  2 3 2
S_{3} 6  2 3  2  2 2 2
7. 1_{k} 5_{i} 2_{+} 0 0 -201 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2 3 2 3 2  2
S_{3} 3  2  3 2 3 2 2 2

Discriminant class: 1

∞ 3 67 a_{1} a_{2} a_{3} Over p = 3 Over p = 67 2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
8. 0_{+} 4_{+} 0_{+} 0 -3  1 1^{3} 4_{+} 1  3 0_{+} 1  3 3 3 3 3  3
C_{3}  3 3  3 3 3  3
9. 0_{+} 0_{+} 2_{+} -1 -22  -5  1^{3} 2_{+} 1  3  3 3 3 3 3 3
C_{3}  3 3 3 3  3
10. 0_{+} 4_{+} 2_{+} 0 -201 -1072 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3 3
C_{3} 3  3  3  3 3  3
11. 0_{+} 4_{+} 2_{+} 0 -201 737 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3  3 3
C_{3} 3  3 3 3 3  3

Discriminant class: 201

∞ 3 67 a_{1} a_{2} a_{3} Over p = 3  Over p = 67  2 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
12. 0_{+} 1_{k} 1_{i} 0 -201  1^{2} 1_{k} 3 3 1^{2} 1_{i} 67∗ 67∗  2  2 2  2
C_{2}  2 2  2 2  2