Low Degree Fields Ramifying Above {17, 19, 29}

Discriminant class: −9367

∞ 17 19 29 a_{1} a_{2} a_{3}  Over p = 17  Over p = 19  Over p = 29 2 3 5 7 11 13 23 31
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
1. 1_{k} 1_{−} 1_{k} 1_{+} 0 9367  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 19 19 1^{2} 1_{+} 29 29  2 2 2  2 2 2
C_{2} 28  2 2 2 2 2 2  2

Discriminant class: −551

∞ 17 19 29 a_{1} a_{2} a_{3} Over p = 17  Over p = 19  Over p = 29  2 3 5 7 11 13 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
2. 1_{k} 2_{+} 1_{k} 1_{−} 0 17 -306 1^{3} 2_{+} ∗  1^{2} 1_{k} 19 19 1^{2} 1_{−} 29∗ 29∗  3 3 2 2 3 3
S_{3}  3  2 2 2 2 2 2

Discriminant class: 17

∞ 17 19 29 a_{1} a_{2} a_{3} Over p = 17 Over p = 19 Over p = 29 2 3 5 7 11 13 23 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
3. 0_{+} 1_{+} 2_{+} 2_{+} 0 -551 -4959 1^{2} 1_{+} 17 17 1^{3} 2_{+} 1 1^{3} 2_{+} ∗ 3 2 2 2 2 3 2 2
S_{3} 3  2 2 3 3 3 3 2