Low Degree Fields Unramified Outside of {∞, 2, 3, 17}

Discriminant class: −102

∞ 2 3 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 17  5 7 11 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} 3_{−} 1_{i} 1_{−} 0 102  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 17∗ 17∗ 2 2 2 2 2  2 2
C_{2} 4  2 2  2
2. 1_{k} 3_{−} 3_{i} 1_{−} 0 -6 -24 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{i} 3∗  1^{2} 1_{−} 17∗ 17∗ 2 2 2 2 2 3 2 2
S_{3} 3 3 2 2 3 3 2
3. 1_{k} 3_{−} 5_{i} 1_{−} 0 -27 -150 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗  1^{2} 1_{−} 17∗ 17∗ 2 2 2 2 2 3 2 2
S_{3}  3 2 2  3 3 2
4. 1_{k} 3_{−} 5_{i} 1_{−} 0 45 -78 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗  1^{2} 1_{−} 17∗ 17∗ 2 2 2 2 2  2 2
S_{3}  3 3 2 2 3 3 3 2
5. 1_{k} 3_{−} 5_{i} 1_{−} 0 27 -90 1^{2} 3_{−} 2∗ 2∗ 1^{3} 5_{i} 3∗  1^{2} 1_{−} 17∗ 17∗ 2 2 2 2 2 3 2 2
S_{3} 3 2 2 3 3 2

Discriminant class: −51

∞ 2 3 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 17  5 7 11 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
6. 1_{k} 0_{+} 1_{k} 1_{−} 0 51  2 0_{+} ∗ ∗ 1^{2} 1_{k} 3 3 1^{2} 1_{−} 17∗ 17∗  2  2
C_{2} 2  2  2 2 2 2
7. 1_{k} 2_{+} 1_{k} 1_{−} -1 1 -3 1^{3} 2_{+} ∗  1^{2} 1_{k} 3 3 1^{2} 1_{−} 17∗ 17∗ 3 2 3 3 3 3  2
S_{3}  2 3 3 2 2 2 2
8. 1_{k} 0_{+} 3_{k} 1_{−} 0 3 -8 2 0_{+} ∗ ∗ 1^{3} 3_{k} 3 1^{2} 1_{−} 17∗ 17∗ 3 2 3 3 3 3 2
S_{3}  2 3 3 2 2 2 2 3
9. 1_{k} 2_{+} 3_{k} 1_{−} 0 -6 -10 1^{3} 2_{+} ∗ 1^{3} 3_{k} 3 1^{2} 1_{−} 17∗ 17∗ 2 3 3 3 3 2
S_{3} 3  2 3 3 2 2 2 2 3
10. 1_{k} 2_{+} 3_{k} 1_{−} 0 6 -6 1^{3} 2_{+} ∗  1^{3} 3_{k} 3  1^{2} 1_{−} 17∗ 17∗ 3 2 3  3  3 2
S_{3} 3  2  2 2 2 2 3

Discriminant class: −34

∞ 2 3 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 17 5 7 11 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
11. 1_{k} 3_{i} 0_{+} 1_{+} 0 34  1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17  2 2
C_{2} 4  2  2 2
12. 1_{k} 3_{i} 4_{+} 1_{+} 0 6 -40 1^{2} 3_{i} −2 −2 1^{3} 4_{+} ∗  1^{2} 1_{+} 17 17  3 2 2 3  3 3
S_{3}  3 2 3 2 2  3 3

Discriminant class: −17

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

Discriminant class: −17 (continued)

∞ 2 3 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 17 5 7 11 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} 2_{i} 4_{+} 1_{+} 0 6 -28 1^{2} 2_{i} −1 −1 1^{3} 4_{+} 1  1^{2} 1_{+} 17 17 2  3 3 2 3 2 3
S_{3} 3  2 2 2 2 3 2 2 2

Discriminant class: −6

∞ 2 3 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 17 5 7 11 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
15. 1_{k} 3_{−} 1_{k} 0_{+} 0 6  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗  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  2 0_{+} ∗ ∗ 3 3 3 2 2 2  3
S_{3}  2 2 2 2 3  2 2
17. 1_{k} 3_{−} 1_{k} 2_{+} -1 -11 39 1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 3 3 1^{3} 2_{+} ∗  3  3 2 2 2 3 3
S_{3}  2 2 2 2 3 3 2 2
18. 1_{k} 3_{−} 3_{k} 2_{+} 0 -51 -170 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{k} 3 1^{3} 2_{+} ∗ 3 2 2 2 3
S_{3} 3  2 2 2 2 3 3 2 2
19. 1_{k} 3_{−} 3_{k} 2_{+} 0 51 34 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  3 3 3 2 2 2 3 3
S_{3} 3  2 2 2 2  3 2 2

Discriminant class: −3

∞ 2 3 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 17 5 7 11 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
20. 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
21. 1_{k} 2_{+} 3_{i} 0_{+} 0 0 -2 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  2 0_{+} ∗ ∗ 2 3 2 3 3 2 2
S_{3}  3 2  2 2 2 3 3
22. 1_{k} 0_{+} 5_{i} 0_{+} 0 0 -3 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 2 3 2 3 3 2 2 3
S_{3}  3 2 3 2 2 2
23. 1_{k} 0_{+} 1_{i} 2_{+} -1 6 -12 2 0_{+} ∗ ∗ 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗  2 3 2 3 3 2 2 3
S_{3}  3 2 3 2 2 2 3 3
24. 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
25. 1_{k} 2_{+} 5_{i} 0_{+} 0 0 -6 1^{3} 2_{+} ∗ 1^{3} 5_{i} 3∗ 2 0_{+} ∗ ∗ 2 2 3 3 2 2 3
S_{3}  2 3 2 2 2 3 3
26. 1_{k} 2_{+} 3_{i} 2_{+} 0 0 -68 1^{3} 2_{+} ∗ 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 2 3 2 3 2 2 3
S_{3} 3  2 3 2 2 2 3
27. 1_{k} 2_{+} 3_{i} 2_{+} 0 0 -34 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  2  2  3 2 2 3
S_{3} 3  3 2 3 2 2 2  3
28. 1_{k} 0_{+} 5_{i} 2_{+} 0 0 -51 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2  3 2 2 3
S_{3} 3  2  2 2 2 3 3
29. 1_{k} 0_{+} 5_{i} 2_{+} 0 0 -153 2 0_{+} ∗ ∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2  2 3  2 2
S_{3} 9  3 2 3 2 2 2 3 3
30. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -306 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2 3 3 2 2
S_{3} 3  2 3 2 2 2  3
31. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -204 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2  2 3 3 2 2 3
S_{3} 12  3 2  2 2 2 3

Discriminant class: −3 (continued)

∞ 2 3 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 17 5 7 11 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
32. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -102 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2 3  2 2 3
S_{3} 3  3 2  2 2 2  3
33. 1_{k} 2_{+} 5_{i} 2_{+} 0 0 -612 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2  3 2 2
S_{3} 6  3 2 3 2 2 2 3

Discriminant class: −2

∞ 2 3 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 17 5 7 11 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
34. 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
35. 1_{k} 3_{i} 4_{+} 0_{+} 0 -3 -10 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  3 0_{+} 1  2 2 3 2 3 2 2 2
S_{3} 3  2 3 3 2 2 3 2 3

Discriminant class: −1

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

Discriminant class: 1

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

Discriminant class: 2

∞ 2 3 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 17 5 7 11 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
39. 0_{+} 3_{+} 0_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗  2  2 2 2  2
C_{2}  2  2  2 2 2 2

Discriminant class: 3

∞ 2 3 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 17 5 7 11 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
40. 0_{+} 2_{i} 1_{k} 0_{+} 0 -3  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 3 3 2 0_{+} ∗ ∗ 2 2  2  2 2
C_{2}  2 2  2  2
41. 0_{+} 2_{i} 3_{k} 2_{+} 0 -51 34 1^{2} 2_{i} −∗ −∗ 1^{3} 3_{k} 3  1^{3} 2_{+} ∗  2 2 3 3 2  2 2
S_{3}  3 2 2 3 2  2

Discriminant class: 6

∞ 2 3 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 17 5 7 11 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
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 -51 -102 1^{2} 3_{k} −2∗ −2∗ 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  3 2 2 2  3  2
S_{3}  2 2 3 3 3 2 2 3
45. 0_{+} 3_{k} 5_{i} 2_{+} 0 -153 102 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2 2 3 3 3 2
S_{3}  2 2 3 3  2 2
46. 0_{+} 3_{k} 5_{i} 2_{+} 0 -153 -714 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 2 2 3

Discriminant class: 17

∞ 2 3 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 17 5 7 11 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
47. 0_{+} 0_{+} 0_{+} 1_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 2 2 2  2 2 2
C_{2}  2 2  2

Discriminant class: 34

∞ 2 3 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 3  Over p = 17 5 7 11 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
48. 0_{+} 3_{+} 0_{+} 1_{+} 0 -34  1^{2} 3_{+} 2 2  1^{2} 1_{+} 17 17  2  2 2 2  2
C_{2} 2  2 2  2 2  2

Discriminant class: 51

∞ 2 3 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 17  5 7 11 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
49. 0_{+} 2_{i} 1_{i} 1_{−} 0 -51  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{−} 17∗ 17∗  2  2 2
C_{2} 2  2  2  2  2 2
50. 0_{+} 2_{i} 5_{i} 1_{−} 0 -27 -48 1^{2} 2_{i} −∗ −∗ 1^{3} 5_{i} 3∗  1^{2} 1_{−} 17∗ 17∗ 3 3 2 3 2 2
S_{3}  2 3 2  2 3 2 2

∞ 2 3 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  Over p = 17  5 7 11 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
51. 0_{+} 3_{k} 1_{k} 1_{−} 0 -102  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 3 3 1^{2} 1_{−} 17∗ 17∗ 2  2  2 2
C_{2} 2  2