Low Degree Fields Ramifying Above {5, 7}

Discriminant class: −35

∞ 5 7 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 2 3 11 13 17 19 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 1_{k} 1_{−} 1_{k} 0 35  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 2  2 2
C_{2} 2  2 2 2 2  2 2 2

Discriminant class: −7

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