Low Degree Fields Unramified Outside of {∞, 5, 61}

Discriminant class: 1

∞ 5 61 a_{1} a_{2} a_{3} Over p = 5  Over p = 61 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 0_{+} 0_{+} 2_{+} -1 -20 9 3 0_{+} 1  1^{3} 2_{+} 1  3  3  3 3 3
C_{3}  3 3  3 3  3

Discriminant class: 5

∞ 5 61 a_{1} a_{2} a_{3} Over p = 5  Over p = 61 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 0_{+} 1_{+} 0_{+} 1 -1  1^{2} 1_{+} 5 5  2 2 2  2 2  2
C_{2}  2  2 2 2

Discriminant class: 61

∞ 5 61 a_{1} a_{2} a_{3} Over p = 5  Over p = 61 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
3. 0_{+} 0_{+} 1_{+} 0 -61  1^{2} 1_{+} 61 61 2  2 2  2  2
C_{2}  2 2 2  2  2 2

Discriminant class: 305

∞ 5 61 a_{1} a_{2} a_{3} Over p = 5  Over p = 61 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
4. 0_{+} 1_{+} 1_{+} 0 -305  1^{2} 1_{+} 5 5 1^{2} 1_{+} 61 61  2  2 2
C_{2} 2  2 2  2  2