Low Degree Fields Ramifying Above {29, 79}

Discriminant class: −2291

∞ 29 79 a_{1} a_{2} a_{3}  Over p = 29  Over p = 79 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 31 37 41 43 47 53 59
1. 1_{k} 1_{−} 1_{k} 0 2291  1^{2} 1_{−} 29∗ 29∗ 1^{2} 1_{k} 79 79 2  2 2  2
C_{2} 18  2  2 2
2. 1_{k} 1_{−} 1_{k} 0  8 -3 1^{2} 1_{−} 29∗ 29∗ 1^{2} 1_{k} 79 79 2  3 2 2 3 3 2
S_{3}  3 2 3 3 3 3 2 2

Discriminant class: −79

∞ 29 79 a_{1} a_{2} a_{3} Over p = 29  Over p = 79  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 31 37 41 43 47 53 59
3. 1_{k} 2_{+} 1_{i} 0 -29 -116 1^{3} 2_{+} ∗  1^{2} 1_{i} 79∗ 79∗  2 3 2  3 2 3
S_{3} 2  3 3 2 2 2 2 2 2