Low Degree Fields Unramified Outside of {∞, 41, 79}

Discriminant class: −3239

∞ 41 79 a_{1} a_{2} a_{3}  Over p = 41  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 43 47 53 59
1. 1_{k} 1_{−} 1_{k} 0 3239  1^{2} 1_{−} 41∗ 41∗ 1^{2} 1_{k} 79 79  2 2  2
C_{2} 70  2 2  2

Discriminant class: −79

∞ 41 79 a_{1} a_{2} a_{3} Over p = 41  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 43 47 53 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 -41 -123 1^{3} 2_{+} ∗  1^{2} 1_{i} 79∗ 79∗ 3 2 3 2 3 3 2 3
S_{3} 2 2 2 2 2 2 2

Discriminant class: 1

∞ 41 79 a_{1} a_{2} a_{3} Over p = 41 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 43 47 53 59
4. 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 3

Discriminant class: 41

∞ 41 79 a_{1} a_{2} a_{3} Over p = 41 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 43 47 53 59
5. 0_{+} 1_{+} 0_{+} 0 -41  1^{2} 1_{+} 41 41 2 0_{+} ∗ ∗  2  2 2 2 2 2
C_{2}  2  2 2