Low Degree Fields Unramified Outside of {∞, 2, 5, 23}

Discriminant class: −230

∞ 2 5 23 a_{1} a_{2} a_{3} Over p = 2 Over p = 5 Over p = 23 3 7 11 13 17 19 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_{+} 1_{k} 0 230  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{+} 5 5 1^{2} 1_{k} 23 23  2
C_{2} 20  2  2 2 2 2  2

Discriminant class: −115

∞ 2 5 23 a_{1} a_{2} a_{3} Over p = 2 Over p = 5 Over p = 23 3 7 11 13 17 19 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
2. 1_{k} 0_{+} 1_{−} 1_{k} 0 115  2 0_{+} ∗ ∗ 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 23 23 2  2 2  2
C_{2} 2  2  2
3. 1_{k} 2_{+} 1_{−} 1_{k} -1 5 -3 1^{3} 2_{+} ∗  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 23 23 2 3 2 2 3 2 3 3
S_{3} 3 3 2 3 3 2 3

Discriminant class: −46

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

Discriminant class: −23

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

Discriminant class: −10

∞ 2 5 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 23 3 7 11 13 17 19 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
7. 1_{k} 3_{k} 1_{−} 0_{+} 0 10  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 5∗ 5∗  2  2  2 2
C_{2} 2  2  2 2

Discriminant class: −5

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

Discriminant class: −2

∞ 2 5 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 23 3 7 11 13 17 19 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
9. 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
10. 1_{k} 3_{i} 2_{+} 0_{+} -1 2 2 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  2 0_{+} ∗ ∗ 3 2 3 2 3 3 2 2
S_{3}  2 3  2 2  2 3
11. 1_{k} 3_{i} 0_{+} 2_{+} -1 -15 -29 1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  3 2  2 3 3 2 2
S_{3}  2  3 2 2 3 2 3
12. 1_{k} 3_{i} 2_{+} 2_{+} -1 -38 -98 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  3 2 3 2  3 2 2
S_{3} 3  2 3 3 2 2 3 2 3
13. 1_{k} 3_{i} 2_{+} 2_{+} -1 77 247 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 3 2 3 2 2
S_{3} 3  2 3 3 2 2 3 2

Discriminant class: −1

∞ 2 5 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 23 3 7 11 13 17 19 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} 0_{+} 0_{+} 0 1  1^{2} 2_{i} −1 −1  2 0_{+} ∗ ∗ 2 2 2  2  2
C_{2}  2 2  2  2
15. 1_{k} 2_{i} 0_{+} 2_{+} -1 8 -6 1^{2} 2_{i} −1 −1 3 0_{+} 1  1^{3} 2_{+} ∗  2 2 2 3  2 3 2
S_{3} 2  3 2 2 3 2 3 2

Discriminant class: 2

∞ 2 5 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 5  Over p = 23 3 7 11 13 17 19 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
16. 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: 5

∞ 2 5 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 5  Over p = 23 3 7 11 13 17 19 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
17. 0_{+} 0_{+} 1_{+} 0_{+} 1 -1  2 0_{+} ∗ ∗ 1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 2 2  2 2
C_{2}  2  2 2 2  2
18. 0_{+} 2_{+} 1_{+} 2_{+} -1 -15 17 1^{3} 2_{+} ∗  1^{2} 1_{+} 5 5 1^{3} 2_{+} ∗  2 2 3 2 2 3  3
S_{3}  2 3 2 2 2  3 2

Discriminant class: 10

∞ 2 5 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 23 3 7 11 13 17 19 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
19. 0_{+} 3_{−} 1_{−} 0_{+} 0 -10  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗  2 2  2 2 2
C_{2} 2  2  2 2

Discriminant class: 23

∞ 2 5 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 23 3 7 11 13 17 19 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. 0_{+} 2_{i} 0_{+} 1_{k} 0 -23  1^{2} 2_{i} −1 −1 2 0_{+} ∗ ∗ 1^{2} 1_{k} 23 23 2  2  2
C_{2}  2  2 2 2 2
21. 0_{+} 2_{i} 2_{+} 1_{k} -1 -8 2 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  1^{2} 1_{k} 23 23 2 3 3 3 2 3 3 2
S_{3}  2 3 3 2 2 2 2

Discriminant class: 46

∞ 2 5 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 23 3 7 11 13 17 19 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
22. 0_{+} 3_{i} 0_{+} 1_{k} 0 -46  1^{2} 3_{i} −2 −2  1^{2} 1_{k} 23 23  2 2 2 2 2 2
C_{2}  2 2  2

Discriminant class: 115

∞ 2 5 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 23  3 7 11 13 17 19 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
23. 0_{+} 2_{i} 1_{−} 1_{i} 0 -115  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{i} 23∗ 23∗  2  2  2
C_{2} 2  2  2 2 2

Discriminant class: 230

∞ 2 5 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 23  3 7 11 13 17 19 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
24. 0_{+} 3_{k} 1_{+} 1_{i} 0 -230  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{+} 5 5 1^{2} 1_{i} 23∗ 23∗ 2 2 2  2 2 2
C_{2} 2  2  2