Low Degree Fields Unramified Outside of {∞, 41, 61}

Discriminant class: 1

∞ 41 61 a_{1} a_{2} a_{3} Over p = 41 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 37 43 47 53 59
1. 0_{+} 0_{+} 2_{+} -1 -20 9  1^{3} 2_{+} 1  3  3 3  3 3 3
C_{3}  3 3  3 3  3

Discriminant class: 41

∞ 41 61 a_{1} a_{2} a_{3} Over p = 41 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 37 43 47 53 59
2. 0_{+} 1_{+} 0_{+} 0 -41  1^{2} 1_{+} 41 41  2  2 2 2 2 2
C_{2}  2  2 2

Discriminant class: 61

∞ 41 61 a_{1} a_{2} a_{3} Over p = 41  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 37 43 47 53 59
3. 0_{+} 0_{+} 1_{+} 0 -61  1^{2} 1_{+} 61 61 2  2 2  2
C_{2}  2 2 2 2 2  2 2

Discriminant class: 2501

∞ 41 61 a_{1} a_{2} a_{3} Over p = 41 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 37 43 47 53 59
4. 0_{+} 1_{+} 1_{+} 0 -2501  1^{2} 1_{+} 41 41 1^{2} 1_{+} 61 61 2 2  2  2
C_{2} 4  2  2 2 2 2  2