Low Degree Fields Ramifying Above {19, 41}

Discriminant class: −779

∞ 19 41 a_{1} a_{2} a_{3}  Over p = 19  Over p = 41  2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 43 47 53 59 61
1. 1_{k} 1_{k} 1_{−} 0 779  1^{2} 1_{k} 19 19 1^{2} 1_{−} 41∗ 41∗ 2  2 2  2
C_{2} 10  2 2  2  2

Discriminant class: −19

∞ 19 41 a_{1} a_{2} a_{3}  Over p = 19  Over p = 41 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 43 47 53 59 61
2. 1_{k} 1_{i} 2_{+} -1 -27 126 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2 3  2 3 3
S_{3} 2  2 2 2 3 3 2 2 3