Low Degree Fields Ramifying Above {5, 17, 23}

Discriminant class: −1955

∞ 5 17 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 23  2 3 7 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} 1_{+} 1_{+} 1_{i} 0 1955  1^{2} 1_{+} 5 5 1^{2} 1_{+} 17 17 1^{2} 1_{i} 23∗ 23∗ 2  2  2 2 2 2
C_{2} 12  2 2  2
2. 1_{k} 1_{+} 1_{+} 1_{i} -1  -5 -8 1^{2} 1_{+} 5 5 1^{2} 1_{+} 17 17 1^{2} 1_{i} 23∗ 23∗ 2 3 2 3 2 2 2 2
S_{3}  2 2 3 2 3 3 3

Discriminant class: −23

∞ 5 17 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 23  2 3 7 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. 1_{k} 2_{+} 2_{+} 1_{i} -1 -28 -233 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3  2 2  2  3
S_{3} 3  2 3 2 3 2 3 2 2
4. 1_{k} 2_{+} 2_{+} 1_{i} -1 -28 107 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 3 2 3
S_{3} 3  2  2 3 2 3 2 2
5. 1_{k} 2_{+} 2_{+} 1_{i} 0 -85 -340 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗  3 2 2 3 2 3 3
S_{3} 3  2 3 2  2 3 2 2

Discriminant class: 5

∞ 5 17 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 17 Over p = 23 2 3 7 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
6. 0_{+} 1_{+} 2_{+} 2_{+} -1 -130 -420 1^{2} 1_{+} 5 5 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 2  2 3 3 3
S_{3}  2  2 2 2 3  2

Discriminant class: 17

∞ 5 17 23 a_{1} a_{2} a_{3} Over p = 5 Over p = 17 Over p = 23 2 3 7 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
7. 0_{+} 2_{+} 1_{+} 2_{+} -1 -38 17 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  3 2 2 2 3  2 2
S_{3}  2 2 3  3 2 3