Low Degree Fields Ramifying Above {19, 29}

Discriminant class: −551

∞ 19 29 a_{1} a_{2} a_{3}  Over p = 19  Over p = 29  2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
1. 1_{k} 1_{k} 1_{−} 0 551  1^{2} 1_{k} 19 19 1^{2} 1_{−} 29∗ 29∗  2 2 2
C_{2} 26  2 2 2 2 2

Discriminant class: −19

∞ 19 29 a_{1} a_{2} a_{3}  Over p = 19  Over p = 29 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
2. 1_{k} 1_{i} 2_{+} -1 10 44 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2 3 3  2
S_{3}  2 2 2 3 3 2 2 3