Low Degree Fields Ramifying Above {13, 17, 23}

Discriminant class: −5083

∞ 13 17 23 a_{1} a_{2} a_{3}  Over p = 13  Over p = 17  Over p = 23 2 3 5 7 11 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 5083  1^{2} 1_{+} 13 13 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 2 2 2 2 2  2
C_{2} 8  2  2 2 2 2

Discriminant class: −391

∞ 13 17 23 a_{1} a_{2} a_{3} Over p = 13  Over p = 17  Over p = 23 2 3 5 7 11 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_{+} 1_{−} 1_{k} -1 -4 51 1^{3} 2_{+} 1  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 3 2 3 3 3 2 2 2
S_{3} 3 3 2 2 2 3 2

Discriminant class: −299

∞ 13 17 23 a_{1} a_{2} a_{3}  Over p = 13  Over p = 17  Over p = 23  2 3 5 7 11 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} 1_{+} 2_{+} 1_{i} -1 23 -46 1^{2} 1_{+} 13 13 1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 2 3 3 3 3 3 3 2
S_{3} 2  3 2 2 2 2 2 2 3

Discriminant class: −23

∞ 13 17 23 a_{1} a_{2}  a_{3} Over p = 13 Over p = 17  Over p = 23  2 3 5 7 11 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
4. 1_{k} 2_{+} 2_{+} 1_{i} -1 74 -352 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗  3 2 2 2 2 3 3
S_{3} 3  2 3 2 3 2  2 2
5. 1_{k} 2_{+} 2_{+} 1_{i} -1 74 -1015 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 2 2
S_{3} 6  2 3 2  2  2 2
6. 1_{k} 2_{+} 2_{+} 1_{i} 0 221 -663 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3  2 2 2 2 3 3
S_{3} 6  2  2 3 2  2 2

Discriminant class: 17

∞ 13 17 23 a_{1} a_{2} a_{3} Over p = 13 Over p = 17 Over p = 23 2 3 5 7 11 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_{+} 0 -299 -598 1^{3} 2_{+} 1  1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  2 2 2 2 3 2 2
S_{3} 3  2 2 3 3 3  2 3