Low Degree Fields Ramifying Above {11, 17, 29}

Discriminant class: −5423

∞ 11 17 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 29 2 3 5 7 13 19 23 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_{i} 1_{+} 1_{+} 0 5423  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29  2  2  2
C_{2} 68  2  2  2

Discriminant class: −11

∞ 11 17 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17 Over p = 29 2 3 5 7 13 19 23 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_{i} 2_{+} 2_{+} -1 -164 1552 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 3 3 2 2 2 3 3
S_{3} 3  3 2 2 3 3  2 3
3. 1_{k} 1_{i} 2_{+} 2_{+} -1 329 1552 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2  3 2 2 2  3
S_{3} 6  2 2 3 3 3 2 3

Discriminant class: 29

∞ 11 17 29 a_{1} a_{2} a_{3} Over p = 11 Over p = 17  Over p = 29 2 3 5 7 13 19 23 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. 0_{+} 2_{+} 2_{+} 1_{+} -1 -249 1586 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 1^{2} 1_{+} 29 29 2 2 3 2 3 2
S_{3} 2  2 2 2 2 3 3 2 3