Quartic Fields Ramifying Above {5, 7}

Discriminant class: 1

∞ 5 7 a_{1} a_{2} a_{3} Over p = 5  Over p = 7 2 3 11 13 17 19 23 29
G h a_{4} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 2_{−} 2_{−} 2_{+} 0 1 0 2^{2} 2_{−} 1 V 2^{2} 2_{+} 1 V 22 22  22 22 22 22
V_{4} 9 22 22 22 22 22 22 22 22

Discriminant class: 5

∞ 5 7 a_{1} a_{2} a_{3} Over p = 5  Over p = 7 2 3 11 13 17 19 23 29
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
2. 0_{+} 3_{−} 2_{−} -1 -9 9 1^{4} 3_{−} 5 5 2^{2} 2_{−} ∗ ∗ 4 4  4 4  4 22
C_{4}  11  22 4 22 4 4 4  22