Low Degree Fields Ramifying Above {5, 13, 17}

Discriminant class: 17

∞ 5 13 17 a_{1} a_{2} a_{3} Over p = 5 Over p = 13 Over p = 17 2 3 7 11 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
1. 0_{+} 2_{+} 2_{+} 1_{+} 0 -65 -195 1^{3} 2_{+} ∗ 1^{3} 2_{+} 1 1^{2} 1_{+} 17 17 3 2 2 2 3 2 2 2
S_{3} 3  2 2 3 3 3 3 2 3

Discriminant class: 1105

∞ 5 13 17 a_{1}  a_{2} a_{3} Over p = 5  Over p = 13  Over p = 17  2 3 7 11 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
2. 0_{+} 1_{+} 1_{−} 1_{−} 0 -1105  1^{2} 1_{+} 5 5 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 17∗ 17∗  2  2  2
C_{2} 4  2  2  2 2 2