Low Degree Fields Ramifying Above {7, 61}

Discriminant class: −427

∞ 7 61 a_{1} a_{2} a_{3} Over p = 7  Over p = 61  2 3 5 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 427  1^{2} 1_{k} 7 7 1^{2} 1_{−} 61∗ 61∗ 2 2 2 2 2  2 2
C_{2} 2  2  2 2 2 2 2

Discriminant class: 1

∞ 7 61 a_{1} a_{2} a_{3} Over p = 7  Over p = 61 2 3 5 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 0_{+} 2_{+} 2_{+} -1 -142 -601 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3  3
C_{3} 3  3 3 3  3  3
3. 0_{+} 2_{+} 2_{+} -1 -142 680 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3  3 3
C_{3} 3  3  3  3 3 3 3