Low Degree Fields Unramified Outside of {∞, 11, 67}

Discriminant class: −67

∞ 11 67 a_{1} a_{2} a_{3} Over p = 11  Over p = 67  2 3 5 7 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} 2_{+} 1_{i} 1 4 -68 1^{3} 2_{+} ∗  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2  3 3
S_{3}  3 2 3 2 2  2 3

Discriminant class: −11

∞ 11 67 a_{1} a_{2} a_{3}  Over p = 11  Over p = 67 2 3 5 7 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 3  1^{2} 1_{i} 11∗ 11∗  2  2 2 2 2
C_{2}  2  2 2
4. 1_{k} 1_{i} 2_{+} -1 45 -72 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} 1  2  3 2 2 2 2
S_{3} 3  2 3 3 2 2 3 3 3

Discriminant class: 1

∞ 11 67 a_{1} a_{2} a_{3} Over p = 11 Over p = 67 2 3 5 7 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 3 0_{+} 1  1^{3} 2_{+} 1  3  3 3 3 3 3
C_{3}  3 3 3 3  3

Discriminant class: 737

∞ 11 67 a_{1} a_{2} a_{3}  Over p = 11  Over p = 67  2 3 5 7 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_{k} 1_{i} 0 -737  1^{2} 1_{k} 11 11 1^{2} 1_{i} 67∗ 67∗  2 2  2 2
C_{2}  2 2  2