Low Degree Fields Ramifying Above {2, 71}

Discriminant class: −142

∞ 2 71 a_{1} a_{2} a_{3} Over p = 2  Over p = 71  3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
1. 1_{k} 3_{+} 1_{i} 0 142  1^{2} 3_{+} 2 2 1^{2} 1_{i} 71∗ 71∗ 2 2 2  2 2 2
C_{2} 4  2 2 2 2 2 2

Discriminant class: −2

∞ 2 71 a_{1} a_{2} a_{3}  Over p = 2  Over p = 71 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 1_{k} 3_{i} 2_{+} -1 -47 163 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  3 2 2 3 2 3 3 2
S_{3}  2 2 2 3 3 2 2 3

Discriminant class: −1

∞ 2 71 a_{1} a_{2} a_{3}  Over p = 2  Over p = 71 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
3. 1_{k} 2_{i} 2_{+} 1 24 -92 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  2 3 2 2  3 2 2
S_{3} 2  2 3 3 2 2 3 2

Discriminant class: 71

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

Discriminant class: 142

∞ 2 71 a_{1} a_{2} a_{3}  Over p = 2  Over p = 71 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
5. 0_{+} 3_{i} 1_{k} 0 -142  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 71 71  2  2  2
C_{2} 3  2  2 2  2
6. 0_{+} 3_{i} 1_{k} -1 -6 -2 1^{2} 3_{i} −2 −2 1^{2} 1_{k} 71 71 3 2 3 2 3 2 3 3
S_{3}  2 3 2 2 3 3  2