Low Degree Fields Ramifying Above {11, 13, 17}

Discriminant class: −2431

∞ 11 13 17 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 17  2 3 5 7 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_{i} 1_{−} 1_{−} 0 2431  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 17∗ 17∗  2  2  2
C_{2} 28  2 2 2  2  2

Discriminant class: −143

∞ 11 13 17 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 17 2 3 5 7 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} 1_{k} 1_{−} 2_{+} -1 6 -80 1^{2} 1_{k} 11 11 1^{2} 1_{−} 13∗ 13∗ 1^{3} 2_{+} ∗  3 2 3 3  2 2
S_{3}  2 3 2 2 3 2 2 2