Low Degree Fields Ramifying Above {7, 97}

Discriminant class: −679

∞ 7 97 a_{1} a_{2} a_{3} Over p = 7  Over p = 97  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_{−} 0 679  1^{2} 1_{k} 7 7 1^{2} 1_{−} 97∗ 97∗  2  2
C_{2} 18  2 2 2  2
2. 1_{k} 1_{k} 1_{−} 0 1 -5 1^{2} 1_{k} 7 7 1^{2} 1_{−} 97∗ 97∗ 3 2  3 3 3 3 2
S_{3}  2 2 2 3 3 2 3 3

Discriminant class: 1

∞ 7 97 a_{1} a_{2} a_{3} Over p = 7  Over p = 97 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
3. 0_{+} 2_{+} 2_{+} 1 -226 503 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3 3 3
C_{3} 3  3  3 3 3 3
4. 0_{+} 2_{+} 2_{+} -1 -226 176 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3  3 3
C_{3} 12  3 3  3 3 3 3 3