Low Degree Fields Unramified Outside of {∞, 79, 89}

Discriminant class: −7031

∞ 79 89 a_{1} a_{2} a_{3}  Over p = 79  Over p = 89 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} 1_{i} 1_{+} 0 7031  1^{2} 1_{i} 79∗ 79∗ 1^{2} 1_{+} 89 89  2 2 2
C_{2} 108  2  2  2 2
2. 1_{k} 1_{i} 1_{+} -1 18 -45 1^{2} 1_{i} 79∗ 79∗ 1^{2} 1_{+} 89 89 3  3 3 2 2 2
S_{3} 2 2 3 3 3 2 2

Discriminant class: −79

∞ 79 89 a_{1} a_{2} a_{3}  Over p = 79  Over p = 89 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 79  1^{2} 1_{i} 79∗ 79∗  2  2  2
C_{2} 5  2  2 2 2 2 2

Discriminant class: 1

∞ 79 89 a_{1} a_{2} a_{3} Over p = 79 Over p = 89 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
4. 0_{+} 2_{+} 0_{+} 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: 89

∞ 79 89 a_{1} a_{2} a_{3} Over p = 79  Over p = 89 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_{+} 1_{+} 0 -89 1^{2} 1_{+} 89 89 2 2 2 2
C_{2}  2 2 2 2 2 2