Low Degree Fields Ramifying Above {5, 13, 23}

Discriminant class: −1495

∞ 5 13 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 13  Over p = 23 2 3 7 11 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_{+} 1_{−} 1_{k} 0 1495  1^{2} 1_{+} 5 5 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{k} 23 23  2 2  2
C_{2} 20  2 2  2 2 2

Discriminant class: −23

∞ 5 13 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 13  Over p = 23  2 3 7 11 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} 2_{+} 2_{+} 1_{i} 0 65 -130 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗  3 2 2 2 2  3
S_{3} 6  2  2 3 2 3 2 2
3. 1_{k} 2_{+} 2_{+} 1_{i} -1 22 -183 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 3  2 2 2 2 3 3
S_{3} 9  2 3 2  2 3 2 2
4. 1_{k} 2_{+} 2_{+} 1_{i} -1 22 -53 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 2 2 3
S_{3} 3  2 3 2 3 2 3 2 2

Discriminant class: 65

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