Low Degree Fields Unramified Outside of {∞, 37, 61}

Discriminant class: 1

∞ 37 61 a_{1} a_{2}  a_{3} Over p = 37 Over p = 61 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. 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
2. 0_{+} 0_{+} 2_{+} -1 -20  9  1^{3} 2_{+} 1  3  3 3  3 3 3
C_{3}  3 3  3 3  3
3. 0_{+} 2_{+} 2_{+} 1 -752 -4096 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3
C_{3} 3  3 3 3 3 3 3
4. 0_{+} 2_{+} 2_{+} -1 -752 -2675 1^{3} 2_{+} 1 1^{3} 2_{+} 1 3 3 3
C_{3} 3  3 3 3 3 3 3 3

Discriminant class: 37

∞ 37 61 a_{1} a_{2} a_{3} Over p = 37 Over p = 61 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
5. 0_{+} 1_{+} 0_{+} 0 -37  1^{2} 1_{+} 37 37 2 0_{+} ∗ ∗ 2  2  2 2 2
C_{2}  2 2 2  2  2

Discriminant class: 61

∞ 37 61 a_{1} a_{2} a_{3} Over p = 37  Over p = 61 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
6. 0_{+} 0_{+} 1_{+} 0 -61  2 0_{+} ∗ ∗ 1^{2} 1_{+} 61 61 2  2 2  2
C_{2}  2 2 2  2  2 2

Discriminant class: 2257

∞ 37 61 a_{1}  a_{2} a_{3}  Over p = 37  Over p = 61  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
7. 0_{+} 1_{−} 1_{−} 0 -2257  1^{2} 1_{−} 37∗ 37∗ 1^{2} 1_{−} 61∗ 61∗  2 2 2 2  2
C_{2} 2  2