Low Degree Fields Unramified Outside of {∞, 61, 79}

Discriminant class: −4819

∞ 61 79 a_{1} a_{2} a_{3}  Over p = 61  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} 1_{−} 1_{k} 0 4819  1^{2} 1_{−} 61∗ 61∗ 1^{2} 1_{k} 79 79 2 2  2
C_{2} 18  2  2  2  2
2. 1_{k} 1_{−} 1_{k} 0  4 -13 1^{2} 1_{−} 61∗ 61∗ 1^{2} 1_{k} 79 79 2 2 3 3 2  3 3
S_{3}  2  2 3 2  2 3

Discriminant class: −79

∞ 61 79 a_{1} a_{2} a_{3} Over p = 61  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} 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

Discriminant class: 1

∞ 61 79 a_{1}  a_{2} a_{3} Over p = 61 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
4. 0_{+} 2_{+} 0_{+} -1 -20  9 1^{3} 2_{+} 1  3 0_{+} 1  3  3 3  3 3 3
C_{3}  3 3  3 3
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
6. 0_{+} 2_{+} 2_{+} 1 -1606 5176 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3  3
C_{3} 3  3  3  3
7. 0_{+} 2_{+} 2_{+} -1 -1606 9281 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3 3 3
C_{3} 12  3 3 3 3  3 3 3

Discriminant class: 61

∞ 61 79 a_{1} a_{2} a_{3} Over p = 61 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
8. 0_{+} 1_{+} 0_{+} 0 -61  1^{2} 1_{+} 61 61 2 0_{+} ∗ ∗ 2  2 2  2
C_{2}  2 2 2 2  2  2