Low Degree Fields Ramifying Above {37, 89}

Discriminant class: 37

∞ 37 89 a_{1} a_{2} a_{3} Over p = 37 Over p = 89 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 41 43 47 53 59
1. 0_{+} 1_{+} 2_{+} -1 -59 -122 1^{2} 1_{+} 37 37 1^{3} 2_{+} ∗  2 3 2 3 3 2 2 2
S_{3} 2 2 2 3 2 3 2

Discriminant class: 3293

∞ 37 89 a_{1}  a_{2} a_{3}  Over p = 37  Over p = 89  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 41 43 47 53 59
2. 0_{+} 1_{−} 1_{−} 0 -3293  1^{2} 1_{−} 37∗ 37∗ 1^{2} 1_{−} 89∗ 89∗ 2 2 2 2  2
C_{2} 2  2