Low Degree Fields Unramified Outside of {∞, 19, 97}

Discriminant class: −1843

∞ 19 97 a_{1} a_{2} a_{3}  Over p = 19  Over p = 97  2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 1843  1^{2} 1_{k} 19 19 1^{2} 1_{−} 97∗ 97∗ 2 2 2 2  2 2
C_{2} 6  2  2
2. 1_{k} 1_{k} 1_{−} -1  1 8 1^{2} 1_{k} 19 19 1^{2} 1_{−} 97∗ 97∗ 2 2 2 2 3 3 2 2
S_{3}  2 3 3 3 3 2 3

Discriminant class: −19

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

Discriminant class: 1

∞ 19 97 a_{1} a_{2} a_{3} Over p = 19 Over p = 97 2 3 5 7 11 13 17 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_{+} 2_{+} 0_{+} -1 -6  7 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3  3 3 3
C_{3}  3  3 3 3 3 3
5. 0_{+} 0_{+} 2_{+} -1 -32 79  1^{3} 2_{+} 1  3 3 3 3 3 3 3 3
C_{3}  3 3 3 3 3  3 3
6. 0_{+} 2_{+} 2_{+} 1 -614 5256 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3
C_{3} 3  3 3 3  3 3
7. 0_{+} 2_{+} 2_{+} 1 -614 3413 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3  3
C_{3} 3  3 3 3 3 3  3

Discriminant class: 97

∞ 19 97 a_{1} a_{2} a_{3} Over p = 19  Over p = 97 2 3 5 7 11 13 17 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
8. 0_{+} 0_{+} 1_{+} 0 -97  2 0_{+} ∗ ∗ 1^{2} 1_{+} 97 97  2 2  2 2 2
C_{2}  2  2 2  2