Low Degree Fields Ramifying Above {2, 31}

Discriminant class: −62

∞ 2 31 a_{1} a_{2} a_{3} Over p = 2  Over p = 31  3 5 7 11 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} 3_{+} 1_{i} 0 62  1^{2} 3_{+} 2 2 1^{2} 1_{i} 31∗ 31∗  2  2 2 2
C_{2} 8  2

Discriminant class: 31

∞ 2 31 a_{1} a_{2} a_{3}  Over p = 2  Over p = 31 3 5 7 11 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_{+} 2_{i} 1_{k} 0 -31  1^{2} 2_{i} −1 −1 1^{2} 1_{k} 31 31  2  2 2 2
C_{2}  2 2  2 2 2 2

Discriminant class: 62

∞ 2 31 a_{1} a_{2} a_{3}  Over p = 2  Over p = 31 3 5 7 11 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
3. 0_{+} 3_{i} 1_{k} 0 -62  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 31 31 2 2 2 2  2
C_{2}  2 2