Low Degree Fields Ramifying Above {5, 7, 13}

Discriminant class: −455

∞ 5 7 13 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 13 2 3 11 17 19 23 29 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_{i} 1_{+} 0 455  1^{2} 1_{+} 5 5 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 13 13  2  2
C_{2} 20  2 2 2  2

Discriminant class: −35

∞ 5 7 13 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 13 2 3 11 17 19 23 29 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} 1_{−} 1_{k} 2_{+} -1 9 -14 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 1^{3} 2_{+} 1 2 3 3 2 2 3 2
S_{3} 3  2 2 2 3 2 2 2 2