Low Degree Fields Ramifying Above {53, 61}

Discriminant class: 61

∞ 53 61 a_{1} a_{2} a_{3} Over p = 53  Over p = 61 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. 0_{+} 2_{+} 1_{+} -1 -35 -2 1^{3} 2_{+} ∗  1^{2} 1_{+} 61 61 2 3 3 2 2 3 2 3
S_{3} 2 2 2 2 3 2 2

Discriminant class: 3233

∞ 53 61 a_{1}  a_{2} a_{3}  Over p = 53  Over p = 61  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. 0_{+} 1_{−} 1_{−} 0 -3233  1^{2} 1_{−} 53∗ 53∗ 1^{2} 1_{−} 61∗ 61∗  2 2 2 2  2 2
C_{2} 2  2  2 2 2  2