Low Degree Fields Ramifying Above {19, 31}

Discriminant class: 1

∞ 19 31 a_{1} a_{2} a_{3} Over p = 19 Over p = 31 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 37 41 43 47 53 59 61
1. 0_{+} 2_{+} 2_{+} 1 -196 829 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3 3 3 3
C_{3} 3  3 3  3 3 3 3 3
2. 0_{+} 2_{+} 2_{+} -1 -196 349 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3  3
C_{3} 3  3 3 3  3  3

Discriminant class: 589

∞ 19 31 a_{1} a_{2} a_{3}  Over p = 19  Over p = 31 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 37 41 43 47 53 59 61
3. 0_{+} 1_{i} 1_{k} 0 -589  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{k} 31 31 2  2  2 2
C_{2}  2 2  2 2