Low Degree Fields Unramified Outside of {∞, 71, 79}

Discriminant class: −79

∞ 71 79 a_{1} a_{2} a_{3} Over p = 71  Over p = 79  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 79  2 0_{+} ∗ ∗ 1^{2} 1_{i} 79∗ 79∗  2  2  2
C_{2} 5  2  2 2 2 2 2
2. 1_{k} 2_{+} 1_{i} -1 24 -121 1^{3} 2_{+} ∗  1^{2} 1_{i} 79∗ 79∗ 3 2 3 2  3 2 3
S_{3}  2  2 2 2 2 2

Discriminant class: −71

∞ 71 79 a_{1} a_{2} a_{3}  Over p = 71  Over p = 79 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 71  1^{2} 1_{i} 71∗ 71∗  2 2 2 2
C_{2} 7  2  2  2  2 2
4. 1_{k} 1_{i} 2_{+} -1 -26 907 1^{2} 1_{i} 71∗ 71∗ 1^{3} 2_{+} 1  3 3 3 2 2 2 2
S_{3} 3 2 3 2 2 3 2 2

Discriminant class: 1

∞ 71 79 a_{1} a_{2} a_{3} Over p = 71 Over p = 79 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_{+} 0_{+} 2_{+} 1 -26 41  1^{3} 2_{+} 1  3 3 3 3 3 3  3
C_{3}  3 3 3 3  3 3 3

Discriminant class: 5609

∞ 71 79 a_{1}  a_{2} a_{3}  Over p = 71  Over p = 79  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
6. 0_{+} 1_{k} 1_{i} 0 -5609  1^{2} 1_{k} 71 71 1^{2} 1_{i} 79∗ 79∗  2  2 2
C_{2}  2 2 2 2  2