Low Degree Fields Unramified Outside of {∞, 53, 67}

Discriminant class: −3551

∞ 53 67 a_{1} a_{2} a_{3}  Over p = 53  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 23 29 31 37 41 43 47 59
1. 1_{k} 1_{−} 1_{k} 0 3551  1^{2} 1_{−} 53∗ 53∗ 1^{2} 1_{k} 67 67  2 2 2  2
C_{2} 58  2  2

Discriminant class: −67

∞ 53 67 a_{1} a_{2} a_{3} Over p = 53  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 23 29 31 37 41 43 47 59
2. 1_{k} 0_{+} 1_{i} 0 67  2 0_{+} ∗ ∗ 1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 2
C_{2} 2 2 2
3. 1_{k} 2_{+} 1_{i} -1 -35 -744 1^{3} 2_{+} ∗  1^{2} 1_{i} 67∗ 67∗ 2 2 2 2 2 2 3
S_{3} 4  3 3 2 3 2 2 3

Discriminant class: 1

∞ 53 67 a_{1} a_{2} a_{3} Over p = 53 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 23 29 31 37 41 43 47 59
4. 0_{+} 0_{+} 2_{+} -1 -22 -5  1^{3} 2_{+} 1  3  3 3 3 3 3
C_{3}  3 3 3 3 3  3

Discriminant class: 53

∞ 53 67 a_{1} a_{2} a_{3} Over p = 53 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 23 29 31 37 41 43 47 59
5. 0_{+} 1_{+} 0_{+} 0 -53  1^{2} 1_{+} 53 53 2 0_{+} ∗ ∗ 2 2 2  2
C_{2}  2  2  2