Low Degree Fields Unramified Outside of {∞, 13, 67}

Discriminant class: −871

∞ 13 67 a_{1} a_{2} a_{3}  Over p = 13  Over p = 67 2 3 5 7 11 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} 0 871  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{k} 67 67  2  2
C_{2} 22  2  2 2 2 2

Discriminant class: −67

∞ 13 67 a_{1} a_{2} a_{3} Over p = 13  Over p = 67  2 3 5 7 11 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
2. 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

Discriminant class: 1

∞ 13 67 a_{1} a_{2} a_{3} Over p = 13 Over p = 67 2 3 5 7 11 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. 0_{+} 2_{+} 0_{+} -1 -4  -1 1^{3} 2_{+} 1  3 0_{+} 1  3 3  3 3 3 3 3
C_{3}  3  3 3 3  3
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
5. 0_{+} 2_{+} 2_{+} 1 -290 1613 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3  3
C_{3} 3  3 3  3 3  3
6. 0_{+} 2_{+} 2_{+} -1 -290 1000 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3
C_{3} 3  3 3  3 3 3  3

Discriminant class: 13

∞ 13 67 a_{1} a_{2} a_{3} Over p = 13 Over p = 67 2 3 5 7 11 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
7. 0_{+} 1_{+} 0_{+} 1 -3  1^{2} 1_{+} 13 13 2 0_{+} ∗ ∗ 2  2 2 2  2
C_{2}  2 2 2  2  2