Low Degree Fields Ramifying Above {7, 17, 23}

Discriminant class: −391

∞ 7 17 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 17  Over p = 23 2 3 5 11 13 19 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} 2_{+} 1_{−} 1_{k} 0 7 -133 1^{3} 2_{+} 1  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 3 2  3 3 2 2 2
S_{3} 3  2 2  2 3 3 2

Discriminant class: −119

∞ 7 17 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 17  Over p = 23 2 3 5 11 13 19 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_{k} 1_{−} 2_{+} 0 23 -23 1^{2} 1_{k} 7 7 1^{2} 1_{−} 17∗ 17∗ 1^{3} 2_{+} ∗  3 3 3 2 2 2 2
S_{3} 5  2 3 3 2 3 2 3 3

Discriminant class: 2737

∞ 7 17 23 a_{1} a_{2} a_{3} Over p = 7 Over p = 17 Over p = 23 2 3 5 11 13 19 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
3. 0_{+} 1_{i} 1_{+} 1_{k} 0 -2737 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 17 17 1^{2} 1_{k} 23 23 2 2 2
C_{2} 2  2 2 2 2 2 2