Low Degree Fields Unramified Outside of {∞, 83, 97}

Discriminant class: −8051

∞ 83 97 a_{1} a_{2} a_{3}  Over p = 83  Over p = 97  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 8051  1^{2} 1_{k} 83 83 1^{2} 1_{−} 97∗ 97∗ 2  2  2
C_{2} 34  2 2  2 2 2 2 2

Discriminant class: −83

∞ 83 97 a_{1} a_{2} a_{3}  Over p = 83  Over p = 97 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 83  1^{2} 1_{i} 83∗ 83∗ 2 0_{+} ∗ ∗ 2  2  2  2
C_{2} 3  2 2 2
3. 1_{k} 1_{i} 0_{+} -1 1 -2 1^{2} 1_{i} 83∗ 83∗ 2 0_{+} ∗ ∗ 2 3 2 3 3 2 3 2
S_{3} 3 3 3 2 2 2

Discriminant class: 1

∞ 83 97 a_{1} a_{2} a_{3} Over p = 83 Over p = 97 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_{+} 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: 97

∞ 83 97 a_{1} a_{2} a_{3} Over p = 83  Over p = 97 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_{+} 0_{+} 1_{+} 0 -97  2 0_{+} ∗ ∗ 1^{2} 1_{+} 97 97  2 2  2 2 2
C_{2}  2 2  2 2