Low Degree Fields Ramifying Above {11, 17, 23}

Discriminant class: −187

∞ 11 17 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 23 2 3 5 7 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_{k} 1_{−} 2_{+} 0 -92 -345 1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 1^{3} 2_{+} ∗  2 2 2 3 2 2 3 2
S_{3} 2 2 2 3 3 3

Discriminant class: −23

∞ 11 17 23 a_{1} a_{2}  a_{3} Over p = 11 Over p = 17  Over p = 23  2 3 5 7 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} 2_{+} 2_{+} 1_{i} -1 -62 277 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 3 2  3
S_{3} 3  2 3 2 3 2 3 2 2
3. 1_{k} 2_{+} 2_{+} 1_{i} -1 -62 -1032 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗  2 2 3 2 3 3
S_{3} 3  2 3 2  2 3 2 2
4. 1_{k} 2_{+} 2_{+} 1_{i} 0 -187 -1309 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2  2 3
S_{3} 3  2  2 3 2 3 2 2

Discriminant class: 4301

∞ 11 17 23 a_{1}  a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 23 2 3 5 7 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
5. 0_{+} 1_{i} 1_{+} 1_{k} 0 -4301  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 17 17 1^{2} 1_{k} 23 23 2 2  2 2  2
C_{2} 2  2  2 2