Low Degree Fields Ramifying Above {5, 7, 23}

Discriminant class: −115

∞ 5 7 23 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 23 2 3 11 13 17 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} 1_{−} 2_{+} 1_{k} 0 7 -28 1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} 1  1^{2} 1_{k} 23 23 2 2 2 2 3 2 3 3
S_{3} 3 3 3 2 3 3 2

Discriminant class: −35

∞ 5 7 23 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 23 2 3 11 13 17 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_{−} 1_{k} 2_{+} -1 -15 40 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 1^{3} 2_{+} ∗ 2 3 3 3 2 2
S_{3} 4  2 2 2 3 2 2 2 2

Discriminant class: 805

∞ 5 7 23 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 23 2 3 11 13 17 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_{+} 1_{i} 1_{k} 0 -805  1^{2} 1_{+} 5 5 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 23 23 2  2  2  2
C_{2} 2  2  2