Low Degree Fields Ramifying Above {61, 83}

Discriminant class: −5063

∞ 61 83 a_{1} a_{2} a_{3}  Over p = 61  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 23 29 31 37 41 43 47 53
1. 1_{k} 1_{+} 1_{i} 0 5063  1^{2} 1_{+} 61 61 1^{2} 1_{i} 83∗ 83∗  2 2 2 2 2 2
C_{2} 36  2 2 2 2  2
2. 1_{k} 1_{+} 1_{i} 0  5 -13 1^{2} 1_{+} 61 61 1^{2} 1_{i} 83∗ 83∗ 3 3 2 2 2 2 2 2
S_{3}  2 2 2 2 3 3 2 3

Discriminant class: −83

∞ 61 83 a_{1} a_{2} a_{3} Over p = 61  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 23 29 31 37 41 43 47 53
3. 1_{k} 2_{+} 1_{i} -1 102 -540 1^{3} 2_{+} 1  1^{2} 1_{i} 83∗ 83∗ 2  2  3 2 3 2
S_{3} 3  3 3 3 3 2 2 2
4. 1_{k} 2_{+} 1_{i} -1 41 -52 1^{3} 2_{+} 1  1^{2} 1_{i} 83∗ 83∗ 2 3 2 3  2  2
S_{3} 12  3 3  3 2 2 2
5. 1_{k} 2_{+} 1_{i} -1 -20 436 1^{3} 2_{+} 1  1^{2} 1_{i} 83∗ 83∗ 2 3 2 3 3 2 3 2
S_{3} 12  3 3 2 2 2