Low Degree Fields Unramified Outside of {∞, 61, 89}

Discriminant class: 1

∞ 61 89 a_{1} a_{2} a_{3} Over p = 61 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. 0_{+} 2_{+} 0_{+} -1 -20 9 1^{3} 2_{+} 1  3  3 3  3 3 3
C_{3}  3 3  3 3

Discriminant class: 61

∞ 61 89 a_{1} a_{2} a_{3} Over p = 61 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. 0_{+} 1_{+} 0_{+} 0 -61  1^{2} 1_{+} 61 61 2 0_{+} ∗ ∗ 2  2 2  2
C_{2}  2 2 2 2  2  2
3. 0_{+} 1_{+} 2_{+} 0 -178 623 1^{2} 1_{+} 61 61 1^{3} 2_{+} ∗  2 3  2 2 3 2 3
S_{3}  2 2 2 2  2 3 2

Discriminant class: 89

∞ 61 89 a_{1} a_{2} a_{3} Over p = 61  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

Discriminant class: 5429

∞ 61 89 a_{1}  a_{2} a_{3}  Over p = 61  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
5. 0_{+} 1_{−} 1_{−} 0 -5429  1^{2} 1_{−} 61∗ 61∗ 1^{2} 1_{−} 89∗ 89∗ 2 2  2 2 2 2
C_{2} 2  2  2