Low Degree Fields Ramifying Above {53, 79}

Discriminant class: −4187

∞ 53 79 a_{1} a_{2} a_{3}  Over p = 53  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 59
1. 1_{k} 1_{−} 1_{k} 0 4187  1^{2} 1_{−} 53∗ 53∗ 1^{2} 1_{k} 79 79 2  2 2  2 2
C_{2} 14  2 2 2 2  2 2 2

Discriminant class: −79

∞ 53 79 a_{1} a_{2} a_{3} Over p = 53  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 59
2. 1_{k} 2_{+} 1_{i} 0 -53 -477 1^{3} 2_{+} ∗  1^{2} 1_{i} 79∗ 79∗ 3 2  2 3 3 2 3
S_{3} 2  2 3 2 2 2 2 2