Low Degree Fields Ramifying Above {61, 71}

Discriminant class: −4331

∞ 61 71 a_{1} a_{2} a_{3}  Over p = 61  Over p = 71 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} 1_{−} 1_{k} 0 4331  1^{2} 1_{−} 61∗ 61∗ 1^{2} 1_{k} 71 71 2  2
C_{2} 34  2  2 2 2 2

Discriminant class: 61

∞ 61 71 a_{1} a_{2} a_{3} Over p = 61 Over p = 71 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_{+} 1_{+} 2_{+} -1 -47 -50 1^{2} 1_{+} 61 61 1^{3} 2_{+} ∗ 2 3 2 2 3 2
S_{3}  2 2 2 2 3 2 3 2