Low Degree Fields Ramifying Above {7, 47}

Discriminant class: −47

∞ 7 47 a_{1} a_{2} a_{3} Over p = 7  Over p = 47  2 3 5 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} 2_{+} 1_{i} -1 -2 -27 1^{3} 2_{+} 1  1^{2} 1_{i} 47∗ 47∗ 3  2 2 2 3 2 2
S_{3} 3  2 2 3 2 2 3 3 3

Discriminant class: −7

∞ 7 47 a_{1} a_{2} a_{3} Over p = 7 Over p = 47 2 3 5 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} 1_{i} 2_{+} -1 16 -7 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  3 2 2 3 2 2 2 3
S_{3} 2  2 3 2 3 3 2 2

Discriminant class: 329

∞ 7 47 a_{1} a_{2} a_{3} Over p = 7 Over p = 47 2 3 5 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_{i} 1_{k} 0 -329  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 47 47  2  2  2  2
C_{2}  2  2  2 2