Low Degree Fields Ramifying Above {5, 11, 17}

Discriminant class: −935

∞ 5 11 17 a_{1} a_{2} a_{3} Over p = 5 Over p = 11 Over p = 17 2 3 7 13 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. 1_{k} 1_{−} 1_{k} 1_{+} 0 935  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 11 11 1^{2} 1_{+} 17 17  2  2  2
C_{2} 28  2 2  2

Discriminant class: −187

∞ 5 11 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 17  2 3 7 13 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. 1_{k} 2_{+} 1_{k} 1_{−} 0 10 -5 1^{3} 2_{+} ∗  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2 3 2 2 2 3 2
S_{3} 4  2 3 2 3  3 3 3