Low Degree Fields Ramifying Above {11, 13, 19}

Discriminant class: −143

∞ 11 13 19 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 19 2 3 5 7 17 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_{k} 1_{−} 2_{+} -1 -44 -107 1^{2} 1_{k} 11 11 1^{2} 1_{−} 13∗ 13∗ 1^{3} 2_{+} 1  3 3 2 3 2 3 2 2
S_{3} 3  2 3 2 2 3 2 2 2

Discriminant class: 2717

∞ 11 13 19 a_{1}  a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 19  2 3 5 7 17 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_{k} 1_{+} 1_{i} 0 -2717  1^{2} 1_{k} 11 11 1^{2} 1_{+} 13 13 1^{2} 1_{i} 19∗ 19∗ 2 2 2  2
C_{2} 2  2 2 2 2  2