Low Degree Fields Unramified Outside of {∞, 53, 79}

Discriminant class: −4187

∞ 53 79 a_{1} a_{2} a_{3}  Over p = 53  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 59
1. 1_{k} 1_{−} 1_{k} 0 4187  1^{2} 1_{−} 53∗ 53∗ 1^{2} 1_{k} 79 79 2  2 2  2 2
C_{2} 14  2 2 2 2  2 2 2

Discriminant class: −79

∞ 53 79 a_{1} a_{2} a_{3} Over p = 53  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 59
2. 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
3. 1_{k} 2_{+} 1_{i} 0 -53 -477 1^{3} 2_{+} ∗  1^{2} 1_{i} 79∗ 79∗ 3 2  2 3 3 2 3
S_{3} 2  2 3 2 2 2 2 2

Discriminant class: 1

∞ 53 79 a_{1} a_{2} a_{3} Over p = 53 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 59
4. 0_{+} 0_{+} 2_{+} 1 -26 41 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3  3
C_{3}  3 3 3 3  3 3 3

Discriminant class: 53

∞ 53 79 a_{1} a_{2} a_{3} Over p = 53 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 59
5. 0_{+} 1_{+} 0_{+} 0 -53  1^{2} 1_{+} 53 53 2 0_{+} ∗ ∗ 2 2 2  2
C_{2}  2  2  2