Low Degree Fields Ramifying Above {5, 19, 23}

Discriminant class: −95

∞ 5 19 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 19  Over p = 23 2 3 7 11 13 17 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_{+} 1_{i} 2_{+} -1 -38 247 1^{2} 1_{+} 5 5 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  3 3 2  2 2 2
S_{3}  3 2 2 2 3 2 3 3

Discriminant class: 5

∞ 5 19 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 19 Over p = 23 2 3 7 11 13 17 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_{+} 2_{+} 2_{+} -1 -291 1926 1^{2} 1_{+} 5 5 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  2 2 2 3 2 2 3 3
S_{3} 3  2 3 2 2 2 3  2

Discriminant class: 2185

∞ 5 19 23 a_{1} a_{2} a_{3} Over p = 5 Over p = 19 Over p = 23 2 3 7 11 13 17 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
3. 0_{+} 1_{−} 1_{k} 1_{k} 0 -2185  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 19 19 1^{2} 1_{k} 23 23  2  2 2
C_{2} 2  2 2  2 2 2 2 2