Low Degree Fields Ramifying Above {5, 7, 17}

Discriminant class: −595

∞ 5 7 17 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 17 2 3 11 13 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_{+} 0 595  1^{2} 1_{+} 5 5 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 17 17 2 2 2  2  2
C_{2} 4  2  2 2  2

Discriminant class: −7

∞ 5 7 17 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 17 2 3 11 13 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} 2_{+} 1_{i} 2_{+} -1 -28 -63 1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  3 2 3 2 2  3 2
S_{3} 3  2  2 3 2 2 3
3. 1_{k} 2_{+} 1_{i} 2_{+} -1 -28 192 1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  2 3 2 2 3  2
S_{3} 3  3 2 3 2 3 2 2 3