Low Degree Fields Unramified Outside of {∞, 2, 11, 29}

Discriminant class: −638

∞ 2 11 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 29 3 5 7 13 17 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_{+} 1_{i} 1_{+} 0 638  1^{2} 3_{+} 2 2 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 29 29  2 2  2  2
C_{2} 20  2 2 2 2 2 2

Discriminant class: −319

∞ 2 11 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 29  3 5 7 13 17 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} 0_{+} 1_{k} 1_{−} 0 319  1^{2} 1_{k} 11 11 1^{2} 1_{−} 29∗ 29∗ 2  2 2  2
C_{2} 10  2  2

Discriminant class: −58

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 29  3 5 7 13 17 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
3. 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
4. 1_{k} 3_{k} 2_{+} 1_{−} 0 -11 -66 1^{2} 3_{k} −2∗ −2∗ 1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2 3
S_{3} 3 2 2 2 3 3 3

Discriminant class: −29

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

Discriminant class: −22

∞ 2 11 29 a_{1} a_{2} a_{3} Over p = 2 Over p = 11 Over p = 29 3 5 7 13 17 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} 3_{−} 1_{k} 0_{+} 0 22  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 11 11  2 2 2  2
C_{2} 2  2 2  2 2  2

Discriminant class: −11

∞ 2 11 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 29 3 5 7 13 17 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} 0_{+} 1_{i} 0_{+} -1 3  2 0_{+} ∗ ∗ 1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗  2 2 2 2
C_{2}  2 2  2
9. 1_{k} 2_{+} 1_{i} 0_{+} -1 1  1 1^{3} 2_{+} ∗  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 3 3 2 2 2 2 3 3
S_{3}  3 2 2  3 2 3
10. 1_{k} 0_{+} 1_{i} 2_{+} -1 -19 44 2 0_{+} ∗ ∗ 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3  2 2 2 2 3 3
S_{3} 2  3 2 2  3 3 2 3
11. 1_{k} 2_{+} 1_{i} 2_{+} 0 -58 -174 1^{3} 2_{+} ∗  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3 2 2 2 2 3 3
S_{3} 3  2 2  3 3 2
12. 1_{k} 2_{+} 1_{i} 2_{+} -1 -19 -43 1^{3} 2_{+} ∗  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3 3 2 2 2 2
S_{3} 3  3 2 2  3  2 3

Discriminant class: −2

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11 Over p = 29 3 5 7 13 17 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} 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
14. 1_{k} 3_{i} 0_{+} 2_{+} -1 10 -14 1^{2} 3_{i} −2 −2 3 0_{+} 1  1^{3} 2_{+} ∗  3 2 2 2  3 2 2
S_{3}  2 3 3 2 2  2

Discriminant class: −1

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11 Over p = 29 3 5 7 13 17 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
15. 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
16. 1_{k} 2_{i} 2_{+} 0_{+} -1 4 2 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  3 0_{+} 1  2 3 2 3 3 2 2 2
S_{3}  3 3 2 2 3 2  2

Discriminant class: 2

∞ 2 11 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 11 Over p = 29 3 5 7 13 17 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_{+} 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
18. 0_{+} 3_{+} 0_{+} 2_{+} -1 -19 15 1^{2} 3_{+} 2 2 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 2 3 2 3 2 3 3
S_{3}  2  2 3 2 2 2 2

Discriminant class: 11 (continued)

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 29 3 5 7 13 17 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

Discriminant class: 11

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

Discriminant class: 22

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 29 3 5 7 13 17 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_{k} 1_{i} 0_{+} 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: 29

∞ 2 11 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 29 3 5 7 13 17 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_{+} 0_{+} 1_{+} 0 -29  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 2  2 2  2
C_{2}  2 2 2 2  2
22. 0_{+} 2_{+} 2_{+} 1_{+} -1 -29 -31 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{+} 29 29 2  3 3 2 2 3 2
S_{3}  2 2 2 2 3 3 2

Discriminant class: 58

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 29  3 5 7 13 17 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
23. 0_{+} 3_{−} 0_{+} 1_{−} 0 -58  1^{2} 3_{−} 2∗ 2∗  1^{2} 1_{−} 29∗ 29∗  2  2 2  2
C_{2} 2  2  2 2 2  2

Discriminant class: 319

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 29  3 5 7 13 17 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_{+} 2_{i} 1_{i} 1_{−} 0 -319  1^{2} 2_{i} −1 −1 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 29∗ 29∗  2  2 2
C_{2} 2  2  2  2  2

Discriminant class: 638

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 29 3 5 7 13 17 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_{+} 3_{i} 1_{k} 1_{+} 0 -638  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 11 11 1^{2} 1_{+} 29 29 2 2  2
C_{2} 2  2  2