Low Degree Fields Ramifying Above {19, 73}

Discriminant class: −1387

∞ 19 73 a_{1} a_{2} a_{3}  Over p = 19  Over p = 73 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 1_{k} 1_{i} 1_{+} 0 1387  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{+} 73 73 2 2 2 2 2  2
C_{2} 4  2 2 2 2

Discriminant class: −19

∞ 19 73 a_{1} a_{2} a_{3}  Over p = 19  Over p = 73 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 1_{k} 1_{i} 2_{+} -1 49 392 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} 1  2 2 3  2 3 3
S_{3} 3  2 2 2 2 3  2 2

Discriminant class: 1

∞ 19 73 a_{1} a_{2} a_{3} Over p = 19 Over p = 73 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
3. 0_{+} 2_{+} 2_{+} 1 -462 3185 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3  3 3
C_{3} 3  3 3  3 3  3
4. 0_{+} 2_{+} 2_{+} -1 -462 976 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3 3
C_{3} 3  3 3 3 3 3  3