Low Degree Fields Ramifying Above {29, 43}

Discriminant class: −1247

∞ 29 43 a_{1} a_{2} a_{3}  Over p = 29  Over p = 43 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 31 37 41 47 53 59 61
1. 1_{k} 1_{−} 1_{k} 0 1247  1^{2} 1_{−} 29∗ 29∗ 1^{2} 1_{k} 43 43  2 2 2  2
C_{2} 26  2  2 2

Discriminant class: −43

∞ 29 43 a_{1} a_{2} a_{3} Over p = 29  Over p = 43  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 31 37 41 47 53 59 61
2. 1_{k} 2_{+} 1_{i} -1 39 -72 1^{3} 2_{+} ∗  1^{2} 1_{i} 43∗ 43∗ 2 2 2 2  3 3 2
S_{3}  3  2 3 3 3 3 2