Low Degree Fields Ramifying Above {17, 79}

Discriminant class: −1343

∞ 17 79 a_{1} a_{2} a_{3}  Over p = 17  Over p = 79 2 3 5 7 11 13 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_{−} 1_{k} 0 1343  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 79 79  2  2  2
C_{2} 34  2  2 2 2 2

Discriminant class: −79

∞ 17 79 a_{1} a_{2} a_{3} Over p = 17  Over p = 79  2 3 5 7 11 13 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. 1_{k} 2_{+} 1_{i} -1 6 56 1^{3} 2_{+} ∗  1^{2} 1_{i} 79∗ 79∗  2 3 2 3 3 3
S_{3}  2  2 2 2 2 2 2