Low Degree Fields Ramifying Above {11, 61}

Discriminant class: −671

∞ 11 61 a_{1} a_{2} a_{3}  Over p = 11  Over p = 61  2 3 5 7 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} 1_{k} 1_{−} 0 671  1^{2} 1_{k} 11 11 1^{2} 1_{−} 61∗ 61∗  2  2 2
C_{2} 30  2 2 2  2 2
2. 1_{k} 1_{k} 1_{−} 0 -1 -5 1^{2} 1_{k} 11 11 1^{2} 1_{−} 61∗ 61∗ 3 3  3 2 3 2 2
S_{3}  2 2 2  3 2 2