Low Degree Fields Ramifying Above {11, 17}

Discriminant class: −187

∞ 11 17 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17  2 3 5 7 13 19 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
1. 1_{k} 1_{k} 1_{−} 0 187  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2 2  2 2 2
C_{2} 2  2 2  2

Discriminant class: −11

∞ 11 17 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17 2 3 5 7 13 19 23 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
2. 1_{k} 1_{i} 2_{+} -1 -11 22 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 3 2 2 2 3 2
S_{3} 3 2 2 3 3 2

Discriminant class: 17

∞ 11 17 a_{1} a_{2} a_{3} Over p = 11  Over p = 17 2 3 5 7 13 19 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 0_{+} 2_{+} 1_{+} 0 -11 -11 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 3 2 2 2 3 3 2 2
S_{3}  2 2 2 3 3  2