Low Degree Fields Unramified Outside of {∞, 5, 67}

Discriminant class: −335

∞ 5 67 a_{1} a_{2} a_{3} Over p = 5 Over p = 67 2 3 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} 1_{−} 1_{k} 0 335  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 67 67  2  2  2
C_{2} 18  2 2 2  2
2. 1_{k} 1_{−} 1_{k} -1 4 1 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 67 67 3 3 3 2  2  2
S_{3}  3 2 2 2 3 2 3 3

Discriminant class: −67

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

Discriminant class: 1

∞ 5 67 a_{1} a_{2} a_{3} Over p = 5  Over p = 67 2 3 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
5. 0_{+} 0_{+} 2_{+} -1 -22 -5  1^{3} 2_{+} 1  3  3 3 3 3 3 3
C_{3}  3 3 3 3  3

Discriminant class: 5

∞ 5 67 a_{1} a_{2} a_{3} Over p = 5  Over p = 67 2 3 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
6. 0_{+} 1_{+} 0_{+} 1 -1  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 2 2 2  2 2  2
C_{2}  2  2 2 2