Low Degree Fields Ramifying Above {31, 43}

Discriminant class: −43

∞ 31 43 a_{1} a_{2} a_{3} Over p = 31  Over p = 43  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 37 41 47 53 59 61
1. 1_{k} 2_{+} 1_{i} -1 21 8 1^{3} 2_{+} 1  1^{2} 1_{i} 43∗ 43∗ 2 2 2 2 3  3 2
S_{3} 3  2 2 3 3 3  2

Discriminant class: 1

∞ 31 43 a_{1} a_{2} a_{3} Over p = 31 Over p = 43 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 37 41 47 53 59 61
2. 0_{+} 2_{+} 2_{+} -1 -444 3604 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3  3
C_{3} 12  3 3 3 3  3 3
3. 0_{+} 2_{+} 2_{+} 1 -444 1728 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3
C_{3} 3  3 3  3  3 3 3

Discriminant class: 1333

∞ 31 43 a_{1}  a_{2} a_{3}  Over p = 31  Over p = 43 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 37 41 47 53 59 61
4. 0_{+} 1_{i} 1_{k} 0 -1333  1^{2} 1_{i} 31∗ 31∗ 1^{2} 1_{k} 43 43 2  2 2 2 2 2 2
C_{2}  2  2