Low Degree Fields Ramifying Above {79, 97}

Discriminant class: −7663

∞ 79 97 a_{1} a_{2} a_{3}  Over p = 79  Over p = 97 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
1. 1_{k} 1_{i} 1_{+} 0 7663  1^{2} 1_{i} 79∗ 79∗ 1^{2} 1_{+} 97 97  2 2  2  2
C_{2} 44  2  2 2 2

Discriminant class: −79

∞ 79 97 a_{1} a_{2} a_{3}  Over p = 79  Over p = 97 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
2. 1_{k} 1_{i} 2_{+} -1 -32 1340 1^{2} 1_{i} 79∗ 79∗ 1^{3} 2_{+} 1  2  2 3 3 2 3
S_{3} 3  3 2 3 2 2 2 2 2

Discriminant class: 1

∞ 79 97 a_{1} a_{2} a_{3} Over p = 79 Over p = 97 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
3. 0_{+} 2_{+} 2_{+} -1 -2554 42856 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3
C_{3} 9  3 3  3  3 3
4. 0_{+} 2_{+} 2_{+} -1 -2554 50519 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3 3 3
C_{3} 63  3  3 3 3 3