Low Degree Fields Ramifying Above {41, 71}

Discriminant class: −2911

∞ 41 71 a_{1} a_{2} a_{3}  Over p = 41  Over p = 71 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 43 47 53 59
1. 1_{k} 1_{−} 1_{k} 0 2911  1^{2} 1_{−} 41∗ 41∗ 1^{2} 1_{k} 71 71  2  2
C_{2} 42  2 2 2  2
2. 1_{k} 1_{−} 1_{k} -1  8 -9 1^{2} 1_{−} 41∗ 41∗ 1^{2} 1_{k} 71 71 3 2 3 3  3 3 2
S_{3} 2  2 2 2  3 3 3 2

Discriminant class: −71

∞ 41 71 a_{1} a_{2} a_{3} Over p = 41  Over p = 71  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 43 47 53 59
3. 1_{k} 2_{+} 1_{i} 0 41 -246 1^{3} 2_{+} ∗  1^{2} 1_{i} 71∗ 71∗  3 2 2 2 2 3
S_{3}  2 3 2 3 3 2 2 2

Discriminant class: 41

∞ 41 71 a_{1} a_{2} a_{3} Over p = 41 Over p = 71 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 43 47 53 59
4. 0_{+} 1_{+} 2_{+} 0 -71 -213 1^{2} 1_{+} 41 41 1^{3} 2_{+} ∗  3 2 3 2 2 2 2 2
S_{3}  3 2 3 3 3 2 2