Low Degree Fields Unramified Outside of {∞, 19, 71}

Discriminant class: −71

∞ 19 71 a_{1} a_{2} a_{3} Over p = 19  Over p = 71  2 3 5 7 11 13 17 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} 0_{+} 1_{i} 0 71  1^{2} 1_{i} 71∗ 71∗  2 2 2 2 2
C_{2} 7  2  2  2 2 2
2. 1_{k} 2_{+} 1_{i} -1 -6 64 1^{3} 2_{+} 1  1^{2} 1_{i} 71∗ 71∗  3 3 2 2 2 2 2
S_{3} 3  2 3 2 3 2 2 2

Discriminant class: −19

∞ 19 71 a_{1} a_{2} a_{3}  Over p = 19  Over p = 71 2 3 5 7 11 13 17 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} 1_{i} 0_{+} -1 5  1^{2} 1_{i} 19∗ 19∗ 2 0_{+} ∗ ∗ 2 2  2
C_{2}  2 2 2 2  2 2
4. 1_{k} 1_{i} 2_{+} -1 -47 234 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2 3 3  2  3
S_{3} 11  2 2 2 2 3  2 2

Discriminant class: 1

∞ 19 71 a_{1} a_{2} a_{3} Over p = 19 Over p = 71 2 3 5 7 11 13 17 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_{+} 2_{+} 0_{+} -1 -6 7 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3  3 3 3
C_{3}  3  3 3 3 3 3

Discriminant class: 1349

∞ 19 71 a_{1}  a_{2} a_{3}  Over p = 19  Over p = 71 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
6. 0_{+} 1_{i} 1_{k} 0 -1349  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{k} 71 71 2 2  2 2  2 2
C_{2}  2  2  2