Low Degree Fields Unramified Outside of {∞, 11, 97}

Discriminant class: −1067

∞ 11 97 a_{1} a_{2} a_{3}  Over p = 11  Over p = 97 2 3 5 7 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. 1_{k} 1_{i} 1_{+} 0 1067  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 97 97 2  2  2
C_{2} 12  2  2  2
2. 1_{k} 1_{i} 1_{+} 0  -4 -7 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 97 97 2 3 2  3 3 3 2
S_{3}  3 3 2  2 3 3 2

Discriminant class: −11

∞ 11 97 a_{1} a_{2} a_{3}  Over p = 11  Over p = 97 2 3 5 7 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. 1_{k} 1_{i} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗  2  2 2 2 2
C_{2}  2  2 2
4. 1_{k} 1_{i} 2_{+} -1 65 -406 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} 1  2 3 3 2 2 2 2 3
S_{3} 3 2 3 2 2 3 3 3

Discriminant class: 1

∞ 11 97 a_{1} a_{2} a_{3} Over p = 11 Over p = 97 2 3 5 7 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
5. 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

∞ 11 97 a_{1} a_{2} a_{3} Over p = 11  Over p = 97 2 3 5 7 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
6. 0_{+} 0_{+} 1_{+} 0 -97  1^{2} 1_{+} 97 97  2 2 2 2 2 2
C_{2}  2  2 2  2