Low Degree Fields Unramified Outside of {∞, 3, 17, 29}

Discriminant class: −1479

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3 Over p = 17 Over p = 29 2 5 7 11 13 19 23 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} 1_{i} 1_{+} 1_{+} 0 1479  1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29  2 2  2
C_{2} 28  2 2  2 2
2. 1_{k} 3_{i} 1_{+} 1_{+} 0  3 -111 1^{3} 3_{i} 3∗  1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29 3  2 2 3 2  3
S_{3}  2 2 3 2 2 3 3
3. 1_{k} 5_{i} 1_{+} 1_{+} 0 27 -396 1^{3} 5_{i} 3∗  1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29  3 2 2 3 2  3
S_{3}  3 2 2  2 2 3 3
4. 1_{k} 5_{i} 1_{+} 1_{+} 0 -27 -207 1^{3} 5_{i} 3∗  1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29 3 3 2 2 3 2
S_{3}  3 2 2 3 2 2 3 3
5. 1_{k} 5_{i} 1_{+} 1_{+} 0 27 -39 1^{3} 5_{i} 3∗ 1^{2} 1_{+} 17 17 1^{2} 1_{+} 29 29 3 3 2 2 2 3
S_{3}  3 2 2 3 2 2

Discriminant class: −87

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 17  Over p = 29  2 5 7 11 13 19 23 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} 1_{k} 0_{+} 1_{−} 0 87  1^{2} 1_{k} 3 3  1^{2} 1_{−} 29∗ 29∗  2  2 2 2
C_{2} 6  2  2  2 2 2
7. 1_{k} 1_{k} 0_{+} 1_{−} -1 2 1 1^{2} 1_{k} 3 3 3 0_{+} 1  1^{2} 1_{−} 29∗ 29∗ 3 2 3 3 3 2 2 2
S_{3} 2 2 3 2 2 2 3

Discriminant class: −51

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 17  Over p = 29 2 5 7 11 13 19 23 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} 1_{k} 1_{−} 0_{+} 0 51  1^{2} 1_{k} 3 3 1^{2} 1_{−} 17∗ 17∗  2  2  2
C_{2} 2  2  2 2 2 2
9. 1_{k} 3_{k} 1_{−} 0_{+} 0 3 -8 1^{3} 3_{k} 3  1^{2} 1_{−} 17∗ 17∗ 3 0_{+} 1  2 3 2  3 3 3 2
S_{3}  2 3 3 2 2 2 2 3

Discriminant class: −3

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3 Over p = 17 Over p = 29 2 5 7 11 13 19 23 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 2 3 3 2 3
S_{3}  3 2 3 2 2 2
12. 1_{k} 1_{i} 2_{+} 0_{+} -1 6 -12 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗ 2 0_{+} ∗ ∗ 2 2 3 2 3 3 2 3
S_{3}  3 2 3 2 2 2 3 3
13. 1_{k} 3_{i} 0_{+} 2_{+} 0 0 -29 1^{3} 3_{i} 3∗ 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗ 2 2 2 3 3 2
S_{3}  2 3 2 2 2 3 3

Discriminant class: −3 (continued)

∞ 3 17 29 a_{1} a_{2}  a_{3}  Over p = 3  Over p = 17 Over p = 29 2 5 7 11 13 19 23 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  -51 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 2 2 3 2  3 2 3
S_{3} 3  2  2 2 2 3 3
15. 1_{k} 5_{i} 2_{+} 0_{+} 0 0 -153 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 2 2  2 3  2
S_{3} 9  3 2 3 2 2 2 3 3
16. 1_{k} 5_{i} 0_{+} 2_{+} 0 0  -87 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 2 3 2 3  2 3
S_{3}  3 2  2 2 2 3 3
17. 1_{k} 5_{i} 0_{+} 2_{+} 0 0 -261 1^{3} 5_{i} 3∗  2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 2 3 2  3 2 3
S_{3}  3 2 3 2 2 2 3 3
18. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -8381 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 2 3 3 2 3
S_{3} 6  3 2  2 2 2  3
19. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -493 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 2  2 3
S_{3} 3  3 2 3 2 2 2 3
20. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -4437 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2  2 3 3 2
S_{3} 6  3 2  2 2 2 3
21. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -42891 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 2 3  2 3
S_{3} 24  2 3 2 2 2  3
22. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -25143 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2  2  3 2
S_{3} 6  3 2 3 2 2 2  3
23. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -1479 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 2 3 3 2 3
S_{3} 6  2 3 2 2 2 3

Discriminant class: 1

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 17 Over p = 29 2 5 7 11 13 19 23 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 17 29 a_{1} a_{2}  a_{3} Over p = 3  Over p = 17  Over p = 29 2 5 7 11 13 19 23 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_{+} 1_{+} 0_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2 2 2  2 2
C_{2}  2 2  2
26. 0_{+} 4_{+} 1_{+} 2_{+} 0 -261 -1044 1^{3} 4_{+} ∗  1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  2 2 2 3  2 2
S_{3}  2 2 3 3  3 2

Discriminant class: 29

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 17  Over p = 29 2 5 7 11 13 19 23 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_{+} 0_{+} 0_{+} 1_{+} 0 -29  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 2  2  2  2
C_{2}  2 2 2 2  2

Discriminant class: 29 (continued)

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 17  Over p = 29 2 5 7 11 13 19 23 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_{+} 4_{+} 0_{+} 1_{+} 0 -12 -13 1^{3} 4_{+} ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 2 3 3 2 2 3 2
S_{3}  2 2 2 2 3 3 2 3

Discriminant class: 493

∞ 3 17 29 a_{1} a_{2} a_{3} Over p = 3  Over p = 17  Over p = 29  2 5 7 11 13 19 23 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_{+} 0_{+} 1_{−} 1_{−} 0 -493  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 2  2 2
C_{2} 2  2 2