Low Degree Fields Ramifying Above {31, 61}

Discriminant class: −1891

∞ 31 61 a_{1} a_{2} a_{3}  Over p = 31  Over p = 61  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 43 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 1891  1^{2} 1_{k} 31 31 1^{2} 1_{−} 61∗ 61∗ 2 2  2  2
C_{2} 10  2

Discriminant class: 1

∞ 31 61 a_{1} a_{2} a_{3} Over p = 31 Over p = 61 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 43 47 53 59
2. 0_{+} 2_{+} 2_{+} 1 -630 5603 1^{3} 2_{+} 1 1^{3} 2_{+} 1 3 3 3 3
C_{3} 3  3 3 3 3 3 3 3
3. 0_{+} 2_{+} 2_{+} -1 -630 5743 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3 3
C_{3} 3  3 3 3  3 3