Low Degree Fields Unramified Outside of {∞, 59, 89}

Discriminant class: −5251

∞ 59 89 a_{1} a_{2} a_{3}  Over p = 59  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 41 43 47 53
1. 1_{k} 1_{k} 1_{−} 0 5251  1^{2} 1_{k} 59 59 1^{2} 1_{−} 89∗ 89∗ 2 2  2 2  2
C_{2} 14  2  2  2

Discriminant class: −59

∞ 59 89 a_{1} a_{2} a_{3}  Over p = 59  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 41 43 47 53
2. 1_{k} 1_{i} 0_{+} 0 59  1^{2} 1_{i} 59∗ 59∗ 2 0_{+} ∗ ∗ 2  2 2
C_{2} 3  2  2 2  2 2
3. 1_{k} 1_{i} 0_{+} 0 2 -1 1^{2} 1_{i} 59∗ 59∗ 2 0_{+} ∗ ∗ 2 3 3 3 2 2  3
S_{3}  2 3 2 2 3 2 2 3

Discriminant class: 89

∞ 59 89 a_{1} a_{2} a_{3} Over p = 59  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 41 43 47 53
4. 0_{+} 0_{+} 1_{+} 0 -89 2 0_{+} ∗ ∗ 1^{2} 1_{+} 89 89 2 2 2 2
C_{2}  2 2 2 2 2 2