Low Degree Fields Unramified Outside of {∞, 3, 11, 17}

Discriminant class: −187

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 17  2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
1. 1_{k} 0_{+} 1_{k} 1_{−} 0 187  2 0_{+} ∗ ∗ 1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2  2 2 2  2
C_{2} 2  2  2
2. 1_{k} 4_{+} 1_{k} 1_{−} 0 6 -23 1^{3} 4_{+} ∗  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2 3 2 2 2 3 2
S_{3} 4 2 3 2 3 3

Discriminant class: −51

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 17  2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
3. 1_{k} 1_{k} 0_{+} 1_{−} 0 51  1^{2} 1_{k} 3 3  1^{2} 1_{−} 17∗ 17∗ 2  2  2
C_{2} 2  2  2 2 2 2
4. 1_{k} 3_{k} 0_{+} 1_{−} 0 3 -8 1^{3} 3_{k} 3  1^{2} 1_{−} 17∗ 17∗ 2 3 2 3 3 3 3 2
S_{3}  2 3 3 2 2 2 2 3

Discriminant class: −11

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 17 2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
5. 1_{k} 0_{+} 1_{i} 0_{+} -1  3  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 2  2 2 2  2
C_{2}  2 2  2
6. 1_{k} 4_{+} 1_{i} 0_{+} 0  6 -1 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 2 3 2 2 2  2 3
S_{3} 3  3 2 2 3 3 3 2 3
7. 1_{k} 0_{+} 1_{i} 2_{+} -1 -11 22 3 0_{+} 1  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 2 2 2 3 2
S_{3}  3 2 2 3  3 2
8. 1_{k} 4_{+} 1_{i} 2_{+} 0 -102 -629 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2  2 2 2 3 2 3
S_{3} 3  2 2 3 3  2 3
9. 1_{k} 4_{+} 1_{i} 2_{+} 0 51 -136 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 2 2 2 3 2 3
S_{3} 9  3 2 2  3 3 2 3

Discriminant class: −3

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3 Over p = 11 Over p = 17 2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
10. 1_{k} 1_{i} 0_{+} 0_{+} 1 1  1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 2 2  2 2
C_{2}  2  2 2 2
11. 1_{k} 5_{i} 0_{+} 0_{+} 0 0  -3 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 2 2 3 3 3 2 2 3
S_{3}  3 2 3 2 2 2
12. 1_{k} 1_{i} 0_{+} 2_{+} -1 6 -12 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 2 3 3 3 2 2 3
S_{3}  3 2 3 2 2 2 3 3
13. 1_{k} 3_{i} 2_{+} 0_{+} 0 0 -11 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 2 2 3 3  2 2 3
S_{3} 2  2  2 2 2  3

Discriminant class: −3 (continued)

∞ 3 11 17 a_{1} a_{2}  a_{3}  Over p = 3  Over p = 11 Over p = 17 2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
14. 1_{k} 5_{i} 2_{+} 0_{+} 0 0 -99 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 2 2  3 2 2 3
S_{3}  3 2 3 2 2 2  3
15. 1_{k} 5_{i} 2_{+} 0_{+} 0 0 -33 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 2 2 3 3 3 2 2
S_{3}  3 2 3 2 2 2  3
16. 1_{k} 5_{i} 0_{+} 2_{+} 0 0 -153 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 2  3  2 2
S_{3} 9  3 2 3 2 2 2 3 3
17. 1_{k} 5_{i} 0_{+} 2_{+} 0 0 -51 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 2 3  3 2 2 3
S_{3} 3  2  2 2 2 3 3
18. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -2057 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2  3 3 2 2 3
S_{3} 3  3 2 3 2 2 2 3 3
19. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -187 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 3 2 2
S_{3} 3  3 2 3 2 2 2 3
20. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -561 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2  3 3 2 2 3
S_{3} 48  2  2 2 2 3
21. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -9537 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3  2 2 3
S_{3} 24  3 2 3 2 2 2 3 3
22. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -1683 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 3 2 2 3
S_{3} 3  3 2 3 2 2 2 3
23. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -6171 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 3 3 2 2
S_{3} 3  2  2 2 2 3 3

Discriminant class: 1

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 11 Over p = 17 2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
24. 0_{+} 4_{+} 0_{+} 0_{+} 0 -3 1 1^{3} 4_{+} 1  3 0_{+} 1  3 3 3 3  3 3 3
C_{3}  3 3 3  3 3 3

Discriminant class: 17

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 17 2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
25. 0_{+} 0_{+} 0_{+} 1_{+} 1 -4  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17  2 2  2 2 2
C_{2}  2 2  2
26. 0_{+} 0_{+} 2_{+} 1_{+} 0 -11 -11 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 3 2 2 3 3 2 2 2
S_{3}  2 2 3 3  2 3

Discriminant class: 33

∞ 3 11 17 a_{1} a_{2} a_{3}  Over p = 3  Over p = 11  Over p = 17 2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
27. 0_{+} 1_{i} 1_{k} 0_{+} 0 -33 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 11 11 2 2 2 2 2
C_{2}  2 2 2 2 2

Discriminant class: 33 (continued)

∞ 3 11 17 a_{1} a_{2} a_{3}  Over p = 3  Over p = 11  Over p = 17 2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
28. 0_{+} 5_{i} 1_{k} 0_{+} 0 -9 -3 1^{3} 5_{i} 3∗ 1^{2} 1_{k} 11 11 3 0_{+} 1 3 2 2 2 2 2 3
S_{3}  3 3 2 2 2 2 2

Discriminant class: 561

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 17 2 5 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
29. 0_{+} 1_{k} 1_{i} 1_{+} 0 -561  1^{2} 1_{k} 3 3 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 17 17  2 2  2 2
C_{2} 2  2 2 2 2 2 2