Low Degree Fields Ramifying Above {127}

Discriminant class: −127

∞ 127 a_{1} a_{2} a_{3}  Over p = 127  2 3 5 7 11 13 17 19
G  h  f^{e} c_{w} d  s 23 29 31 37 41 43 47 53
1. 1_{k} 1_{i} 0 127  1^{2} 1_{i} 127∗ 127∗  2 2 2
C_{2} 5  2 2  2  2

Discriminant class: 1

∞ 127 a_{1} a_{2} a_{3} Over p = 127 2 3 5 7 11 13 17 19
G  h  f^{e} c_{w} d s 23 29 31 37 41 43 47 53
2. 0_{+} 2_{+} -1 -42 -80 1^{3} 2_{+} 1  3  3 3 3 3
C_{3}  3 3 3 3 3 3  3