Low Degree Fields Unramified Outside of {∞, 13, 79}

Discriminant class: −1027

∞ 13 79 a_{1} a_{2} a_{3}  Over p = 13  Over p = 79  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_{i} 0 1027  1^{2} 1_{+} 13 13 1^{2} 1_{i} 79∗ 79∗ 2 2 2  2 2 2
C_{2} 4  2 2  2  2

Discriminant class: −79

∞ 13 79 a_{1} a_{2} a_{3} Over p = 13  Over p = 79  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 79  1^{2} 1_{i} 79∗ 79∗  2  2  2
C_{2} 5  2  2 2 2 2 2 2
3. 1_{k} 2_{+} 1_{i} 0 13 -13 1^{3} 2_{+} 1  1^{2} 1_{i} 79∗ 79∗ 3 2 3 2 3 2 3 3
S_{3} 3  2 3 2 2 2 2 2 2

Discriminant class: 1

∞ 13 79 a_{1} a_{2} a_{3} Over p = 13 Over p = 79 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
4. 0_{+} 2_{+} 0_{+} -1 -4  -1 1^{3} 2_{+} 1  3 3  3 3 3 3 3
C_{3}  3  3 3 3  3
5. 0_{+} 0_{+} 2_{+} 1 -26 41 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3  3 3
C_{3}  3 3 3  3 3 3 3
6. 0_{+} 2_{+} 2_{+} -1 -342 -989 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3  3 3
C_{3} 3  3 3 3  3 3
7. 0_{+} 2_{+} 2_{+} 1 -342 2016 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3  3
C_{3} 3  3 3  3 3 3 3 3

Discriminant class: 13

∞ 13 79 a_{1} a_{2} a_{3} Over p = 13 Over p = 79 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
8. 0_{+} 1_{+} 0_{+} 1 -3  1^{2} 1_{+} 13 13  2  2 2 2  2
C_{2}  2 2 2  2  2
9. 0_{+} 1_{+} 2_{+} 0 -79 -158 1^{2} 1_{+} 13 13 1^{3} 2_{+} 1  2 3 2 2 2 3 2
S_{3} 3  3 2 2 2 3 2 3 2