Low Degree Fields Ramifying Above {67, 79}

Discriminant class: −79

∞ 67 79 a_{1} a_{2} a_{3} Over p = 67  Over p = 79  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
1. 1_{k} 2_{+} 1_{i} -1 -22 129 1^{3} 2_{+} 1  1^{2} 1_{i} 79∗ 79∗ 3 2 3 2 3 3 2 3
S_{3} 6  2 3 2 2 2 2 2

Discriminant class: 1

∞ 67 79 a_{1} a_{2} a_{3} Over p = 67 Over p = 79 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
2. 0_{+} 2_{+} 2_{+} 1 -1764 -196 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3
C_{3} 3  3  3 3  3
3. 0_{+} 2_{+} 2_{+} 1 -1764 15683 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3 3
C_{3} 3  3 3 3 3 3 3 3

Discriminant class: 5293

∞ 67 79 a_{1}  a_{2} a_{3}  Over p = 67  Over p = 79 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
4. 0_{+} 1_{i} 1_{k} 0 -5293  1^{2} 1_{i} 67∗ 67∗ 1^{2} 1_{k} 79 79 2  2  2 2 2
C_{2}  2 2 2  2