Low Degree Fields Unramified Outside of {∞, 59, 71}

Discriminant class: −71

∞ 59 71 a_{1} a_{2} a_{3} Over p = 59  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 41 43 47 53
1. 1_{k} 0_{+} 1_{i} 0 71  2 0_{+} ∗ ∗ 1^{2} 1_{i} 71∗ 71∗  2 2 2 2
C_{2} 7  2  2  2  2 2
2. 1_{k} 2_{+} 1_{i} -1 20 83 1^{3} 2_{+} ∗  1^{2} 1_{i} 71∗ 71∗ 3 3 3 2 2 2 2 3
S_{3}  2 3 2 3 2 3 2 2

Discriminant class: −59

∞ 59 71 a_{1} a_{2} a_{3}  Over p = 59  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 41 43 47 53
3. 1_{k} 1_{i} 0_{+} 0 59  1^{2} 1_{i} 59∗ 59∗  2  2 2
C_{2} 3  2  2 2  2 2
4. 1_{k} 1_{i} 0_{+} 0 2 -1 1^{2} 1_{i} 59∗ 59∗  2 3 3 3 2 2  3
S_{3}  2 3 2 2 3 2 2 3

Discriminant class: 4189

∞ 59 71 a_{1}  a_{2} a_{3}  Over p = 59  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 41 43 47 53
5. 0_{+} 1_{k} 1_{i} 0 -4189  1^{2} 1_{k} 59 59 1^{2} 1_{i} 71∗ 71∗ 2  2  2
C_{2}  2 2 2  2