Low Degree Fields Ramifying Above {11, 17, 19}

Discriminant class: −323

∞ 11 17 19 a_{1} a_{2} a_{3} Over p = 11  Over p = 17  Over p = 19  2 3 5 7 13 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} 2_{+} 1_{+} 1_{i} 0 -22 -55 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗ 2 3 2 2 2 2
S_{3} 3 3 3 2 2 2 2

Discriminant class: 3553

∞ 11 17 19 a_{1}  a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 19 2 3 5 7 13 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_{k} 0 -3553  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 19 19  2  2 2
C_{2} 2  2 2  2 2  2