Low Degree Fields Unramified Outside of {∞, 11, 41}

Discriminant class: −451

∞ 11 41 a_{1} a_{2} a_{3}  Over p = 11  Over p = 41  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 43 47 53 59 61
1. 1_{k} 1_{k} 1_{−} 0 451  1^{2} 1_{k} 11 11 1^{2} 1_{−} 41∗ 41∗ 2 2
C_{2} 6 2 2 2 2
2. 1_{k} 1_{k} 1_{−} -1 -5 8 1^{2} 1_{k} 11 11 1^{2} 1_{−} 41∗ 41∗ 2 2 3 3  3 3 3
S_{3}  3 3 3 2 2 2 3 2

Discriminant class: −11

∞ 11 41 a_{1} a_{2} a_{3}  Over p = 11  Over p = 41 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 43 47 53 59 61
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
4. 1_{k} 1_{i} 2_{+} -1 14 44 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 3 2 2 2 2
S_{3} 2 3 2 3 3 3 2

Discriminant class: 41

∞ 11 41 a_{1} a_{2} a_{3} Over p = 11  Over p = 41 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 43 47 53 59 61
5. 0_{+} 0_{+} 1_{+} 0 -41  2 0_{+} ∗ ∗ 1^{2} 1_{+} 41 41  2  2 2 2 2
C_{2}  2  2 2