Low Degree Fields Ramifying Above {5, 47}

Discriminant class: −235

∞ 5 47 a_{1} a_{2} a_{3} Over p = 5 Over p = 47 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 53 59 61
1. 1_{k} 1_{−} 1_{k} 0 235  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 47 47 2 2 2 2  2 2
C_{2} 2  2 2 2 2  2

Discriminant class: −47

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

Discriminant class: 5

∞ 5 47 a_{1} a_{2} a_{3} Over p = 5  Over p = 47 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 53 59 61
3. 0_{+} 1_{+} 2_{+} 1 -31 -40 1^{2} 1_{+} 5 5 1^{3} 2_{+} ∗  2 2 2 3 2 2 3 2
S_{3}  3 3 2 3 2 2 3 3