Low Degree Fields Unramified Outside of {∞, 3, 79}

Discriminant class: −79

∞ 3 79 a_{1} a_{2} a_{3} Over p = 3  Over p = 79  2 5 7 11 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 79  2 0_{+} ∗ ∗ 1^{2} 1_{i} 79∗ 79∗  2  2
C_{2} 5  2  2 2 2 2 2 2
2. 1_{k} 4_{+} 1_{i} 0 9 -45 1^{3} 4_{+} ∗  1^{2} 1_{i} 79∗ 79∗ 3  2  3 2  3
S_{3} 2  2 3 2 2 2 2 2 2

Discriminant class: −3

∞ 3 79 a_{1} a_{2} a_{3} Over p = 3 Over p = 79 2 5 7 11 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 1  1^{2} 1_{i} 3∗ 3∗  2 2  2  2  2
C_{2}  2  2  2 2 2
4. 1_{k} 5_{i} 0_{+} 0 0 -3 1^{3} 5_{i} 3∗  3 0_{+} 1  2 2 3 2 3 2 3 2
S_{3}  2 3 3 2 3 2 2 2
5. 1_{k} 3_{i} 2_{+} 0 0 -79 1^{3} 3_{i} 3∗ 1^{3} 2_{+} 1 2 2 3 2 2 3 2
S_{3} 6  2 3 3 2 3 2 2 2
6. 1_{k} 5_{i} 2_{+} 0 0 -711 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2 3 2 3 2  2
S_{3} 3  2  2 3 2 2 2
7. 1_{k} 5_{i} 2_{+} 0 0 -237 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2  2 3 2 3 2
S_{3} 3  2 3 3 2  2 2 2

Discriminant class: 1

∞ 3 79 a_{1} a_{2} a_{3} Over p = 3  Over p = 79 2 5 7 11 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
8. 0_{+} 4_{+} 0_{+} 0 -3  1 1^{3} 4_{+} 1  3 0_{+} 1  3 3 3 3 3  3
C_{3}  3 3  3 3 3  3
9. 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
10. 0_{+} 4_{+} 2_{+} 0 -237 316 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3 3  3
C_{3} 12  3  3 3  3 3 3
11. 0_{+} 4_{+} 2_{+} 0 -237 1027 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3  3 3
C_{3} 3  3 3 3 3  3

Discriminant class: 237

∞ 3 79 a_{1} a_{2} a_{3} Over p = 3  Over p = 79  2 5 7 11 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
12. 0_{+} 1_{k} 1_{i} 0 -237  1^{2} 1_{k} 3 3 1^{2} 1_{i} 79∗ 79∗ 2 2 2 2  2
C_{2}  2  2