Low Degree Fields Ramifying Above {19, 79}

Discriminant class: −79

∞ 19 79 a_{1} a_{2} a_{3} Over p = 19  Over p = 79  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} 2_{+} 1_{i} -1 -6 -31 1^{3} 2_{+} 1  1^{2} 1_{i} 79∗ 79∗ 3 2 3 2 3  2 3
S_{3} 3  2  2 2 2 2 2 2

Discriminant class: 1

∞ 19 79 a_{1} a_{2} a_{3} Over p = 19 Over p = 79 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. 0_{+} 2_{+} 2_{+} -1 -500 4225 1^{3} 2_{+} 1 1^{3} 2_{+} 1 3 3 3 3 3 3
C_{3} 3  3 3 3 3 3 3 3 3
3. 0_{+} 2_{+} 2_{+} -1 -500 2724 1^{3} 2_{+} 1 1^{3} 2_{+} 1 3 3 3 3 3
C_{3} 3  3 3 3

Discriminant class: 1501

∞ 19 79 a_{1}  a_{2} a_{3}  Over p = 19  Over p = 79 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
4. 0_{+} 1_{i} 1_{k} 0 -1501  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{k} 79 79 2  2  2 2
C_{2}  2  2 2