Low Degree Fields Unramified Outside of {∞, 41, 89}

Discriminant class: 41

∞ 41 89 a_{1} a_{2} a_{3} Over p = 41 Over p = 89 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_{+} 1_{+} 0_{+} 0 -41  1^{2} 1_{+} 41 41 2 0_{+} ∗ ∗  2  2 2 2 2 2
C_{2}  2  2 2

Discriminant class: 89

∞ 41 89 a_{1} a_{2} a_{3} Over p = 41  Over p = 89 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_{+} 0_{+} 1_{+} 0 -89  2 0_{+} ∗ ∗ 1^{2} 1_{+} 89 89  2  2  2  2
C_{2}  2 2 2 2 2  2

Discriminant class: 3649

∞ 41 89 a_{1}  a_{2} a_{3}  Over p = 41  Over p = 89  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_{+} 1_{−} 1_{−} 0 -3649  1^{2} 1_{−} 41∗ 41∗ 1^{2} 1_{−} 89∗ 89∗  2  2
C_{2} 2  2  2 2 2 2 2 2