Low Degree Fields Ramifying Above {17, 23, 29}

Discriminant class: −11339

∞ 17 23 29 a_{1}  a_{2} a_{3}  Over p = 17  Over p = 23  Over p = 29  2 3 5 7 11 13 19 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_{k} 1_{−} 0 11339  1^{2} 1_{+} 17 17 1^{2} 1_{k} 23 23 1^{2} 1_{−} 29∗ 29∗ 2  2
C_{2} 52  2  2 2  2 2

Discriminant class: −391

∞ 17 23 29 a_{1} a_{2} a_{3}  Over p = 17  Over p = 23  Over p = 29 2 3 5 7 11 13 19 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_{−} 1_{k} 2_{+} -1 68 -275 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 1^{3} 2_{+} ∗  3 2  3  3 2 2
S_{3}  3 2 2  2 3 3 2

Discriminant class: 17

∞ 17 23 29 a_{1} a_{2} a_{3} Over p = 17 Over p = 23 Over p = 29 2 3 5 7 11 13 19 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. 0_{+} 1_{+} 2_{+} 2_{+} -1 -222 -1087 1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  3 2 2 2 2 3 3 2
S_{3}  2 2 3  3  2 3

Discriminant class: 493

∞ 17 23 29 a_{1} a_{2} a_{3}  Over p = 17  Over p = 23  Over p = 29  2 3 5 7 11 13 19 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_{+} 1_{−} 2_{+} 1_{−} 0 -46 -69 1^{2} 1_{−} 17∗ 17∗ 1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 2  2 2 3 3 2 3
S_{3}  3  2 2 3 3 3 3