Low Degree Fields Ramifying Above {23, 83}

Discriminant class: −23

∞ 23 83 a_{1} a_{2} a_{3}  Over p = 23  Over p = 83 2 3 5 7 11 13 17 19
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} 2_{+} 0 83 -249 1^{2} 1_{i} 23∗ 23∗ 1^{3} 2_{+} ∗  3  2 2 2 3 2 2
S_{3} 3  3  2 3 2  2 3
2. 1_{k} 1_{i} 2_{+} -1 28 292 1^{2} 1_{i} 23∗ 23∗ 1^{3} 2_{+} ∗  3 2 2 2 3 2 2
S_{3} 3  3 3 2 3 2 3 2 3
3. 1_{k} 1_{i} 2_{+} -1 28 43 1^{2} 1_{i} 23∗ 23∗ 1^{3} 2_{+} ∗  3 3 2 2 2  2 2
S_{3} 3  3 2  2 3 2 3

Discriminant class: 1909

∞ 23 83 a_{1}  a_{2} a_{3}  Over p = 23  Over p = 83 2 3 5 7 11 13 17 19
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 -1909  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{k} 83 83 2  2 2 2 2
C_{2}  2  2