Low Degree Fields Unramified Outside of {∞, 37, 79}

Discriminant class: −2923

∞ 37 79 a_{1} a_{2} a_{3}  Over p = 37  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 41 43 47 53 59
1. 1_{k} 1_{−} 1_{k} 0 2923  1^{2} 1_{−} 37∗ 37∗ 1^{2} 1_{k} 79 79 2 2 2 2  2  2
C_{2} 6  2  2 2  2 2
2. 1_{k} 1_{−} 1_{k} -1 14 -12 1^{2} 1_{−} 37∗ 37∗ 1^{2} 1_{k} 79 79 2 2 2 2 3 2 3 2
S_{3} 2 2 2 3 2 2 3

Discriminant class: −79

∞ 37 79 a_{1} a_{2} a_{3} Over p = 37  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 41 43 47 53 59
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

∞ 37 79 a_{1} a_{2}  a_{3} Over p = 37 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 41 43 47 53 59
4. 0_{+} 2_{+} 0_{+} 1 -12  11 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3  3 3 3
C_{3}  3  3 3
5. 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
6. 0_{+} 2_{+} 2_{+} 1 -974 11259 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3  3 3
C_{3} 3  3 3 3 3 3 3  3
7. 0_{+} 2_{+} 2_{+} 1 -974 8336 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3
C_{3} 21  3 3 3 3 3 3 3

Discriminant class: 37

∞ 37 79 a_{1} a_{2} a_{3} Over p = 37 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 41 43 47 53 59
8. 0_{+} 1_{+} 0_{+} 0 -37  1^{2} 1_{+} 37 37 2 0_{+} ∗ ∗ 2  2  2 2 2
C_{2}  2 2 2  2  2