Low Degree Fields Unramified Outside of {∞, 11, 61}

Discriminant class: −671

∞ 11 61 a_{1} a_{2} a_{3}  Over p = 11  Over p = 61  2 3 5 7 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. 1_{k} 1_{k} 1_{−} 0 671  1^{2} 1_{k} 11 11 1^{2} 1_{−} 61∗ 61∗  2  2 2
C_{2} 30  2 2 2  2 2
2. 1_{k} 1_{k} 1_{−} 0 -1 -5 1^{2} 1_{k} 11 11 1^{2} 1_{−} 61∗ 61∗ 3 3  3 2 3 2 2
S_{3} 2 2 2 3 2 2

Discriminant class: −11

∞ 11 61 a_{1} a_{2} a_{3}  Over p = 11  Over p = 61 2 3 5 7 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. 1_{k} 1_{i} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 2  2 2 2 2
C_{2}  2  2 2

Discriminant class: 1

∞ 11 61 a_{1} a_{2} a_{3} Over p = 11 Over p = 61 2 3 5 7 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_{+} 0_{+} 2_{+} -1 -20 9  1^{3} 2_{+} 1  3  3 3 3 3 3
C_{3}  3 3  3 3  3

Discriminant class: 61

∞ 11 61 a_{1} a_{2} a_{3} Over p = 11  Over p = 61 2 3 5 7 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
5. 0_{+} 0_{+} 1_{+} 0 -61  2 0_{+} ∗ ∗ 1^{2} 1_{+} 61 61 2  2  2  2
C_{2}  2 2 2  2  2 2