Low Degree Fields Unramified Outside of {∞, 2, 3, 11}

Discriminant class: −66

∞ 2 3 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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} 3_{i} 1_{i} 1_{k} 0 66  1^{2} 3_{i} −2 −2 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 11 11  2  2 2
C_{2} 8  2  2  2
2. 1_{k} 3_{i} 3_{i} 1_{k} 0 -9 -14 1^{2} 3_{i} −2 −2 1^{3} 3_{i} 3∗  1^{2} 1_{k} 11 11 3  3 3 2 3 2 2
S_{3}  2 3 2  3 2 3 3
3. 1_{k} 3_{i} 5_{i} 1_{k} 0 -9 -30 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  1^{2} 1_{k} 11 11  3 3 3 2 3 2 2
S_{3}  2  2  2 3 3
4. 1_{k} 3_{i} 5_{i} 1_{k} 0 18 -48 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  1^{2} 1_{k} 11 11 3 3 3 3 2  2 2
S_{3}  2 3 2  3 2 3
5. 1_{k} 3_{i} 5_{i} 1_{k} 0 -27 -78 1^{2} 3_{i} −2 −2 1^{3} 5_{i} 3∗  1^{2} 1_{k} 11 11 3 3  2 3 2 2
S_{3}  2 3 2  3 2  3

Discriminant class: −33

∞ 2 3 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 11  5 7 13 17 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
6. 1_{k} 2_{i} 1_{k} 1_{i} 0 33  1^{2} 2_{i} −1 −1 1^{2} 1_{k} 3 3 1^{2} 1_{i} 11∗ 11∗ 2  2  2
C_{2} 4  2  2 2
7. 1_{k} 2_{i} 3_{k} 1_{i} 0 6 -12 1^{2} 2_{i} −1 −1 1^{3} 3_{k} 3  1^{2} 1_{i} 11∗ 11∗ 2 3 2 3  3 3 2
S_{3}  3 3 3 3 2 3 2 2

Discriminant class: −22

∞ 2 3 11 a_{1} a_{2} a_{3} Over p = 2 Over p = 3 Over p = 11 5 7 13 17 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
8. 1_{k} 3_{−} 0_{+} 1_{k} 0 22  1^{2} 3_{−} 2∗ 2∗ 2 0_{+} ∗ ∗ 1^{2} 1_{k} 11 11 2 2  2
C_{2} 2  2 2  2 2  2
9. 1_{k} 3_{−} 4_{+} 1_{k} 0 6 -32 1^{2} 3_{−} 2∗ 2∗ 1^{3} 4_{+} ∗  1^{2} 1_{k} 11 11 2 2  2 3 3 3 3
S_{3}  2 2 3 3 2 2 3 2

Discriminant class: −11

∞ 2 3 11 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 11  5 7 13 17 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} 0_{+} 0_{+} 1_{i} -1 3  2 0_{+} ∗ ∗  1^{2} 1_{i} 11∗ 11∗  2 2 2 2  2
C_{2}  2 2  2
11. 1_{k} 2_{+} 0_{+} 1_{i} -1 1 1 1^{3} 2_{+} ∗  3 0_{+} 1  1^{2} 1_{i} 11∗ 11∗ 3 2 2 2 2 3 2 3
S_{3}  3 2 2  3 2 3
12. 1_{k} 0_{+} 4_{+} 1_{i} 0 6 -1 2 0_{+} ∗ ∗ 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 3 2 2 2 2  2 3
S_{3} 3  3 2 2 3 3 3 2 3
13. 1_{k} 2_{+} 4_{+} 1_{i} 0 -12 -28 1^{3} 2_{+} ∗  1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 3 2 2 2 2 3 2
S_{3} 3  2 2 3 3  2 3

Discriminant class: −11 (continued)

∞ 2 3 11 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 11  5 7 13 17 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} 2_{+} 4_{+} 1_{i} 0 6 -10 1^{3} 2_{+} ∗  1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗  2 2 2 2 3 2 3
S_{3} 3  3 2 2 3 3 3 2

Discriminant class: −6

∞ 2 3 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
15. 1_{k} 3_{−} 1_{k} 0_{+} 0 6  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 3 3  2 2 2 2
C_{2} 2  2 2 2 2  2 2
16. 1_{k} 3_{−} 3_{k} 0_{+} 0 3 -2 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{k} 3  3 0_{+} 1  3 3 2 2 2 2  3
S_{3}  2 2 2 2 3  2 2

Discriminant class: −3

∞ 2 3 11 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
17. 1_{k} 0_{+} 1_{i} 0_{+} 1 1  2 0_{+} ∗ ∗ 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 2  2  2 2
C_{2}  2  2 2 2
18. 1_{k} 2_{+} 3_{i} 0_{+} 0 0 -2 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  2 0_{+} ∗ ∗ 2 3 3 2 3 2 2
S_{3}  3 2  2 2 2 3 3
19. 1_{k} 0_{+} 5_{i} 0_{+} 0 0 -3 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 2 3 3 2 3 2 2 3
S_{3}  3 2 3 2 2 2
20. 1_{k} 2_{+} 5_{i} 0_{+} 0 0 -6 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 2 0_{+} ∗ ∗ 2 3 2 3 2 2 3
S_{3}  2 3 2 2 2 3 3
21. 1_{k} 2_{+} 5_{i} 0_{+} 0 0 -12 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 2 0_{+} ∗ ∗ 2 3 2 2 2 3
S_{3}  3 2 3 2 2 2 3 3
22. 1_{k} 2_{+} 1_{i} 2_{+} -1 -7 13 1^{3} 2_{+} ∗  1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗  2 3  2 3 2 2 3
S_{3}  3 2  2 2 2 3 3
23. 1_{k} 0_{+} 3_{i} 2_{+} 0 0 -11 2 0_{+} ∗ ∗ 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  2 3 3 2  2 2 3
S_{3} 2  2  2 2 2  3
24. 1_{k} 2_{+} 3_{i} 2_{+} 0 0 -22 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  2  3 2 3 2 2 3
S_{3} 3  3 2  2 2 2 3
25. 1_{k} 0_{+} 5_{i} 2_{+} 0 0 -33 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 3 2 3 2 2
S_{3}  3 2 3 2 2 2  3
26. 1_{k} 0_{+} 5_{i} 2_{+} 0 0 -99 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2  2 3 2 2 3
S_{3}  3 2 3 2 2 2  3
27. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -198 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 3 2  2 2 3
S_{3} 6  3 2 3 2 2 2 3
28. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -66 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 2 3 2 3 2 2
S_{3} 6  2 3 2 2 2 3
29. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -132 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 2 3 2 2 2
S_{3} 3  3 2 3 2 2 2 3 3
30. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -396 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 2 3 3 2 3 2 2 3
S_{3} 3  2 3 2 2 2 3 3

Discriminant class: −2

∞ 2 3 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
31. 1_{k} 3_{i} 0_{+} 0_{+} 0 2  1^{2} 3_{i} −2 −2  2 2 2  2 2 2
C_{2}  2  2 2  2
32. 1_{k} 3_{i} 4_{+} 0_{+} 0 -3 -10 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  3 0_{+} 1  2 2 2 3 3 2 2 2
S_{3} 3  2 3 3 2 2 3 2 3

Discriminant class: −1

∞ 2 3 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
33. 1_{k} 2_{i} 0_{+} 0_{+} 0 1  1^{2} 2_{i} −1 −1 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗  2  2 2  2
C_{2}  2 2  2  2
34. 1_{k} 2_{i} 4_{+} 0_{+} 0 -3 -4 1^{2} 2_{i} −1 −1 1^{3} 4_{+} ∗  2 0_{+} ∗ ∗ 3 2 3 3 2 2 3 2
S_{3}  3  2 2  2 3 2
35. 1_{k} 2_{i} 0_{+} 2_{+} -1 4  2 1^{2} 2_{i} −1 −1 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  3 2 3 3 2 2 3 2
S_{3}  3 3 2 2 3 2  2
36. 1_{k} 2_{i} 4_{+} 2_{+} 0 33 -176 1^{2} 2_{i} −1 −1 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  2 3  2 2 3 2
S_{3} 3  3 3 2 2 3 2 3 2
37. 1_{k} 2_{i} 4_{+} 2_{+} 0 33 -22 1^{2} 2_{i} −1 −1 1^{3} 4_{+} ∗ 1^{3} 2_{+} ∗ 3 2 3 2 2 2
S_{3} 6  3 2 2 3 2 3 2

Discriminant class: 1

∞ 2 3 11 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
38. 0_{+} 0_{+} 4_{+} 0_{+} 0 -3 1 3 0_{+} 1  1^{3} 4_{+} 1  3 0_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3  3 3 3

Discriminant class: 2

∞ 2 3 11 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
39. 0_{+} 3_{+} 0_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 2  2  2  2
C_{2}  2  2  2 2 2 2
40. 0_{+} 3_{+} 4_{+} 2_{+} 0 -66 -176 1^{2} 3_{+} 2 2 1^{3} 4_{+} ∗  1^{3} 2_{+} ∗  2 3 2 3 2 3 2 3
S_{3}  2  2  2 2 2 2

Discriminant class: 3

∞ 2 3 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
41. 0_{+} 2_{i} 1_{k} 0_{+} 0 -3  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 3 3  2 2  2 2  2 2
C_{2}  2 2  2  2

Discriminant class: 6

∞ 2 3 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
42. 0_{+} 3_{k} 1_{i} 0_{+} 0 -6  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗  2 2 2  2
C_{2}  2 2  2 2
43. 0_{+} 3_{k} 5_{i} 0_{+} 0 -9 -6 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 3 2 2 2 3 3 3 2
S_{3}  2 2  3 3 2 2 3
44. 0_{+} 3_{k} 3_{i} 2_{+} 0 -33 -66 1^{2} 3_{k} −2∗ −2∗ 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  3 2 2 2 3  3 2
S_{3}  2 2 3  2 2
45. 0_{+} 3_{k} 5_{i} 2_{+} 0 -99 66 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  3 2 2 2  3 3 2
S_{3}  2 2 3 3 3 2 2 3
46. 0_{+} 3_{k} 5_{i} 2_{+} 0 -99 -330 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 2 2 2 3 3 2
S_{3}  2 2 3 3 3 2 2 3

Discriminant class: 11

∞ 2 3 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
47. 0_{+} 2_{i} 0_{+} 1_{k} 0 -11  1^{2} 2_{i} −∗ −∗ 2 0_{+} ∗ ∗ 1^{2} 1_{k} 11 11  2 2  2 2 2
C_{2}  2  2  2 2 2

Discriminant class: 22

∞ 2 3 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 11  5 7 13 17 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
48. 0_{+} 3_{k} 0_{+} 1_{i} 0 -22  1^{2} 3_{k} −2∗ −2∗  1^{2} 1_{i} 11∗ 11∗ 2  2 2 2  2
C_{2}  2 2 2 2 2

Discriminant class: 33

∞ 2 3 11 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 11 5 7 13 17 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
49. 0_{+} 0_{+} 1_{i} 1_{k} 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
50. 0_{+} 0_{+} 5_{i} 1_{k} 0 -9 -3 3 0_{+} 1 1^{3} 5_{i} 3∗ 1^{2} 1_{k} 11 11 2 2 2 3 2 2 3
S_{3}  3 3 2 2 2 2 2

Discriminant class: 66

∞ 2 3 11 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 11  5 7 13 17 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
51. 0_{+} 3_{+} 1_{k} 1_{i} 0 -66  1^{2} 3_{+} 2 2 1^{2} 1_{k} 3 3 1^{2} 1_{i} 11∗ 11∗  2  2 2
C_{2} 2  2  2  2