Low Degree Fields Unramified Outside of {∞, 2, 23, 29}

Discriminant class: −1334

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29  3 5 7 11 13 17 19 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 1334  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{−} 29∗ 29∗  2 2 2  2 2
C_{2} 32  2 2 2 2  2 2

Discriminant class: −667

∞ 2 23 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 23  Over p = 29 3 5 7 11 13 17 19 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_{i} 1_{+} 0 667  2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2  2
C_{2} 4  2  2 2  2
3. 1_{k} 2_{+} 1_{i} 1_{+} 0 -2 -10 1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2  3 3 3 2
S_{3}  3 2 3 2 2 3  2

Discriminant class: −58

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29  3 5 7 11 13 17 19 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 8 132 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 3 2 3 3

Discriminant class: −46

∞ 2 23 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 23  Over p = 29 3 5 7 11 13 17 19 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_{+} 1_{i} 0_{+} 0 46  1^{2} 3_{+} 2 2 1^{2} 1_{i} 23∗ 23∗ 2 0_{+} ∗ ∗ 2  2  2 2
C_{2} 4  2
7. 1_{k} 3_{+} 1_{i} 2_{+} -1 -19 -449 1^{2} 3_{+} 2 2 1^{2} 1_{i} 23∗ 23∗ 1^{3} 2_{+} ∗  2 3 2 3 2 2 3 3
S_{3} 3 3 2 3

Discriminant class: −29

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29 3 5 7 11 13 17 19 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} 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
9. 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: −23

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

Discriminant class: −2

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23 Over p = 29 3 5 7 11 13 17 19 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
12. 1_{k} 3_{i} 0_{+} 0_{+} 0  2  1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗  2 2  2  2
C_{2}  2  2 2  2
13. 1_{k} 3_{i} 2_{+} 0_{+} -1 -15 -29 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 3 2 2  2 3 3 2
S_{3}  2  3 2 2 3 2 3
14. 1_{k} 3_{i} 0_{+} 2_{+} -1 10 -14 1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  3 2 2 3 2  3 2
S_{3}  2 3 3 2 2  2
15. 1_{k} 3_{i} 2_{+} 2_{+} -1 445 247 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  3 2 2 3 2 3  2
S_{3} 3  2 3 3 2 2 3 2 3
16. 1_{k} 3_{i} 2_{+} 2_{+} -1 -222 3582 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 2 3 3 2
S_{3} 3  2 3  2 2 3 2 3

Discriminant class: −1

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23 Over p = 29 3 5 7 11 13 17 19 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} 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
18. 1_{k} 2_{i} 2_{+} 0_{+} -1 8 -6 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  3 0_{+} 1  2 3 2 2 3  2 2
S_{3} 2  3 2 2 3 2 3 2

Discriminant class: 2

∞ 2 23 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 23 Over p = 29 3 5 7 11 13 17 19 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_{+} 0_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2  2 0_{+} ∗ ∗ 2 2  2 2  2
C_{2}  2  2  2 2 2 2
20. 0_{+} 3_{+} 0_{+} 2_{+} -1 -19 15 1^{2} 3_{+} 2 2 3 0_{+} 1  1^{3} 2_{+} ∗  2 2 3 2 2 3 2 3
S_{3}  2  2 3 2 2 2 2

Discriminant class: 23 (continued)

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29 3 5 7 11 13 17 19 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: 23

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

Discriminant class: 29

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

Discriminant class: 46

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29 3 5 7 11 13 17 19 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_{i} 1_{k} 0_{+} 0 -46  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 23 23 2 0_{+} ∗ ∗  2 2 2 2 2
C_{2}  2 2  2

Discriminant class: 58

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29  3 5 7 11 13 17 19 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_{+} 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: 667

∞ 2 23 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29 3 5 7 11 13 17 19 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_{+} 2_{i} 1_{k} 1_{+} 0 -667  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 23 23 1^{2} 1_{+} 29 29  2  2  2
C_{2} 2  2 2  2 2

Discriminant class: 1334

∞ 2 23 29 a_{1}  a_{2} a_{3}  Over p = 2  Over p = 23  Over p = 29  3 5 7 11 13 17 19 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
26. 0_{+} 3_{k} 1_{k} 1_{−} 0 -1334  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 23 23 1^{2} 1_{−} 29∗ 29∗ 2  2
C_{2} 2  2 2  2 2