Low Degree Fields Ramifying Above {13, 17, 19}

Discriminant class: −4199

∞ 13 17 19 a_{1} a_{2} a_{3}  Over p = 13  Over p = 17  Over p = 19 2 3 5 7 11 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_{+} 1_{k} 0 4199  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{+} 17 17 1^{2} 1_{k} 19 19  2  2
C_{2} 88  2 2  2 2  2

Discriminant class: 17

∞ 13 17 19 a_{1} a_{2} a_{3} Over p = 13 Over p = 17 Over p = 19 2 3 5 7 11 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_{+} 2_{+} 1_{+} 2_{+} -1 -82 -183 1^{3} 2_{+} 1  1^{2} 1_{+} 17 17 1^{3} 2_{+} 1  3 2 2 2 2 2 2 2
S_{3} 9  2 2 3 3  3 2