Low Degree Fields Unramified Outside of {∞, 5, 97}

Discriminant class: 1

∞ 5 97 a_{1} a_{2} a_{3} Over p = 5  Over p = 97 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
1. 0_{+} 0_{+} 2_{+} -1 -32 79 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3  3
C_{3}  3 3 3 3 3  3 3

Discriminant class: 5

∞ 5 97 a_{1} a_{2} a_{3} Over p = 5  Over p = 97 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
2. 0_{+} 1_{+} 0_{+} 1 -1  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 2 2 2  2 2  2
C_{2}  2  2 2 2

Discriminant class: 97

∞ 5 97 a_{1} a_{2} a_{3} Over p = 5  Over p = 97 2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
3. 0_{+} 0_{+} 1_{+} 0 -97  2 0_{+} ∗ ∗ 1^{2} 1_{+} 97 97  2  2 2 2 2
C_{2}  2  2 2  2

Discriminant class: 485

∞ 5 97 a_{1} a_{2} a_{3}  Over p = 5  Over p = 97  2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
4. 0_{+} 1_{−} 1_{−} 0 -485  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 97∗ 97∗ 2 2  2
C_{2} 2  2  2 2 2 2 2