Low Degree Fields Unramified Outside of {∞, 13, 43}

Discriminant class: −559

∞ 13 43 a_{1} a_{2} a_{3}  Over p = 13  Over p = 43  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 47 53 59 61
1. 1_{k} 1_{+} 1_{i} 0 559  1^{2} 1_{+} 13 13 1^{2} 1_{i} 43∗ 43∗  2  2
C_{2} 16  2 2  2 2  2 2

Discriminant class: −43

∞ 13 43 a_{1} a_{2} a_{3} Over p = 13  Over p = 43  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 47 53 59 61
2. 1_{k} 0_{+} 1_{i} 0 43  1^{2} 1_{i} 43∗ 43∗ 2 2 2 2  2
C_{2}  2  2  2
3. 1_{k} 2_{+} 1_{i} -1 -17 38 1^{3} 2_{+} 1  1^{2} 1_{i} 43∗ 43∗ 2 2 2 2 3 3 2 3
S_{3} 3 2 3 2 3 2

Discriminant class: 1

∞ 13 43 a_{1} a_{2} a_{3} Over p = 13 Over p = 43 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 47 53 59 61
4. 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
5. 0_{+} 0_{+} 2_{+} -1 -14 -8 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3  3  3
6. 0_{+} 2_{+} 2_{+} -1 -186 -911 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3  3
C_{3} 3  3 3 3  3 3 3
7. 0_{+} 2_{+} 2_{+} 1 -186 -207 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3  3  3
C_{3} 3  3 3  3  3 3

Discriminant class: 13

∞ 13 43 a_{1} a_{2} a_{3} Over p = 13 Over p = 43 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 47 53 59 61
8. 0_{+} 1_{+} 0_{+} 1 -3  1^{2} 1_{+} 13 13  2  2 2 2  2
C_{2}  2 2 2 2  2