Low Degree Fields Ramifying Above {2, 79}

Discriminant class: −158

∞ 2 79 a_{1} a_{2} a_{3} Over p = 2  Over p = 79  3 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} 3_{+} 1_{i} 0 158  1^{2} 3_{+} 2 2 1^{2} 1_{i} 79∗ 79∗  2 2 2 2 2 2
C_{2} 8  2  2

Discriminant class: 2

∞ 2 79 a_{1} a_{2} a_{3} Over p = 2  Over p = 79 3 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. 0_{+} 3_{+} 2_{+} -1 -26 38 1^{2} 3_{+} 2 2 1^{3} 2_{+} 1  2 2 3 2 2 3 2 3
S_{3} 3 2 2 3 2 2 2

Discriminant class: 79

∞ 2 79 a_{1} a_{2} a_{3}  Over p = 2  Over p = 79 3 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. 0_{+} 2_{i} 1_{k} 0 -79  1^{2} 2_{i} −1 −1 1^{2} 1_{k} 79 79  2  2 2 2
C_{2} 3  2 2 2 2  2
4. 0_{+} 2_{i} 1_{k} -1 -4 2 1^{2} 2_{i} −1 −1 1^{2} 1_{k} 79 79 3 3 3 2 3 2 2 2
S_{3} 2 2 2 2 3 2 3

Discriminant class: 158

∞ 2 79 a_{1} a_{2} a_{3}  Over p = 2  Over p = 79 3 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_{+} 3_{i} 1_{k} 0 -158  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 79 79 2 2  2 2  2
C_{2}  2  2 2  2