Low Degree Fields Ramifying Above {23, 89}

Discriminant class: −2047

∞ 23 89 a_{1} a_{2} a_{3}  Over p = 23  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 29 31 37 41 43 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 2047  1^{2} 1_{k} 23 23 1^{2} 1_{−} 89∗ 89∗  2 2  2 2 2
C_{2} 18  2 2  2  2 2
2. 1_{k} 1_{k} 1_{−} 0  7 -5 1^{2} 1_{k} 23 23 1^{2} 1_{−} 89∗ 89∗ 3 2 2 3 2 2 2 3
S_{3}  2 2 3 2  3 2 2