Low Degree Fields Ramifying Above {11, 31}

Discriminant class: −11

∞ 11 31 a_{1} a_{2} a_{3}  Over p = 11  Over p = 31 2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 37 41 43 47 53 59 61
1. 1_{k} 1_{i} 2_{+} -1 21 -54 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} 1  2  3 2 2 2 2 3
S_{3} 3  2 3 2 2 3 3 3 2

Discriminant class: 341

∞ 11 31 a_{1} a_{2} a_{3}  Over p = 11  Over p = 31  2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 37 41 43 47 53 59 61
2. 0_{+} 1_{k} 1_{i} 0 -341  1^{2} 1_{k} 11 11 1^{2} 1_{i} 31∗ 31∗ 2 2  2  2 2
C_{2}  2 2  2