Quartic Fields Ramifying Above {29, 43}

Discriminant class: 1

∞ 29 43 a_{1} a_{2} a_{3} Over p = 29  Over p = 43 2 3 5 7 11 13 17 19
G h a_{4} f^{e} c_{w} d s f^{e} c_{w} d s 23 31 37 41 47 53 59 61
1. 2_{−} 2_{−} 2_{+} 0 7 0 2^{2} 2_{−} 1 V 2^{2} 2_{+} 1 V 22 22 22 22 22  22 22
V_{4} 13 324 22 22 22 22 22

Discriminant class: 29

∞ 29 43 a_{1} a_{2} a_{3}  Over p = 29  Over p = 43 2 3 5 7 11 13 17 19
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d s 23 31 37 41 47 53 59 61
2. 0_{+} 3_{−} 2_{−}  1 -315 -937 1^{4} 3_{−} 29 29 2^{2} 2_{−} ∗ ∗ 4 4  22 4 22 4 4
C_{4}  2575  4 4 4 4  4