Low Degree Fields Unramified Outside of {∞, 2, 17, 29}

Discriminant class: −986

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29 3 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} 3_{k} 1_{−} 1_{+} 0 986  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{+} 29 29  2 2  2
C_{2} 44  2  2  2  2

Discriminant class: −493

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29  3 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
2. 1_{k} 2_{i} 1_{−} 1_{−} 0 493  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 29∗ 29∗ 2 2  2  2
C_{2} 12  2  2
3. 1_{k} 2_{i} 1_{−} 1_{−} 0 10 -12 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 3 2 3 3  2
S_{3} 5  3 3 3 3 3 2 3 2

Discriminant class: −58

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29  3 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
4. 1_{k} 3_{k} 0_{+} 1_{−} 0 58  1^{2} 3_{k} −2∗ −2∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2
C_{2} 2 2 2 2
5. 1_{k} 3_{k} 2_{+} 1_{−} -1 -11 -97 1^{2} 3_{k} −2∗ −2∗ 1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2
S_{3} 13  3 2 2 3 2 3 3 3

Discriminant class: −34

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29 3 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} 3_{i} 1_{+} 0_{+} 0 34  1^{2} 3_{i} −2 −2 1^{2} 1_{+} 17 17  2  2 2
C_{2} 4  2  2 2

Discriminant class: −29

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29 3 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
7. 1_{k} 2_{i} 0_{+} 1_{+} 0 29  1^{2} 2_{i} −∗ −∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29  2  2
C_{2} 6  2 2  2 2 2
8. 1_{k} 2_{i} 0_{+} 1_{+} -1 0 -2 1^{2} 2_{i} −∗ −∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 3 3 2 3 3  2 3
S_{3}  2 2 3 3 3 2 2 2

Discriminant class: −17

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29 3 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
9. 1_{k} 2_{i} 1_{+} 0_{+} 0 17  1^{2} 2_{i} −1 −1 1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2  2
C_{2} 4  2 2 2 2  2 2 2
10. 1_{k} 2_{i} 1_{+} 2_{+} 0 29 -174 1^{2} 2_{i} −1 −1 1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  2 3 3 3 2 3
S_{3}  2 2 2 2 3 2 2 2

Discriminant class: −2

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17 Over p = 29 3 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
11. 1_{k} 3_{i} 0_{+} 0_{+} 0 2  1^{2} 3_{i} −2 −2  2 0_{+} ∗ ∗  2 2  2  2 2
C_{2}  2  2 2  2
12. 1_{k} 3_{i} 0_{+} 2_{+} -1 10 -14 1^{2} 3_{i} −2 −2  1^{3} 2_{+} ∗  3 2 2 3 2 3 2 2
S_{3}  2 3 3 2 2  2

Discriminant class: −1

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17 Over p = 29 3 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
13. 1_{k} 2_{i} 0_{+} 0_{+} 0 1  1^{2} 2_{i} −1 −1  2  2 2  2 2 2
C_{2}  2 2  2  2

Discriminant class: 2

∞ 2 17 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 17 Over p = 29 3 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. 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
15. 0_{+} 3_{+} 0_{+} 2_{+} -1 -19 15 1^{2} 3_{+} 2 2 3 0_{+} 1  1^{3} 2_{+} ∗  2 2 3 2 2 2 3 3
S_{3}  2  2 3 2 2 2 2

Discriminant class: 17

∞ 2 17 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 29 3 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
16. 0_{+} 0_{+} 1_{+} 0_{+} 1 -4  1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗ 2 2 2 2  2 2
C_{2}  2 2  2

Discriminant class: 29

∞ 2 17 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 29 3 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
17. 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
18. 0_{+} 2_{+} 2_{+} 1_{+} -1 -45 -97 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{+} 29 29 2 3 3 2 3 2 3 2
S_{3}  2 2 2 2 3  2 3

Discriminant class: 34

∞ 2 17 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 29 3 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
19. 0_{+} 3_{+} 1_{+} 0_{+} 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: 58

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29  3 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
20. 0_{+} 3_{−} 0_{+} 1_{−} 0 -58  1^{2} 3_{−} 2∗ 2∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 29∗ 29∗  2  2  2
C_{2} 2  2  2 2 2  2

Discriminant class: 493

∞ 2 17 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 29  3 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
21. 0_{+} 0_{+} 1_{−} 1_{−} 0 -493  2 0_{+} ∗ ∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 29∗ 29∗  2 2  2 2
C_{2} 2  2 2

Discriminant class: 986

∞ 2 17 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 29 3 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
22. 0_{+} 3_{−} 1_{−} 1_{+} 0 -986  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{+} 29 29 2  2 2 2  2
C_{2} 4  2  2 2 2 2 2