Low Degree Fields Unramified Outside of {∞, 29, 41}

Discriminant class: 29

∞ 29 41 a_{1} a_{2} a_{3} Over p = 29 Over p = 41 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 31 37 43 47 53 59 61
1. 0_{+} 1_{+} 0_{+} 0 -29  1^{2} 1_{+} 29 29 2 0_{+} ∗ ∗ 2 2  2  2 2
C_{2}  2 2 2 2  2
2. 0_{+} 1_{+} 2_{+} -1 -27 44 1^{2} 1_{+} 29 29 1^{3} 2_{+} ∗  2 2 3 3 2 3 2 2
S_{3} 2 2 2 2 3 2

Discriminant class: 41

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

Discriminant class: 1189

∞ 29 41 a_{1}  a_{2} a_{3}  Over p = 29  Over p = 41  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d  s 23 31 37 43 47 53 59 61
4. 0_{+} 1_{−} 1_{−} 0 -1189  1^{2} 1_{−} 29∗ 29∗ 1^{2} 1_{−} 41∗ 41∗ 2  2  2
C_{2} 2  2 2 2  2  2