Low Degree Fields Ramifying Above {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} 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
2. 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
3. 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
4. 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

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
5. 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
6. 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

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
7. 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