Low Degree Fields Unramified Outside of {∞, 2, 17, 23}

Discriminant class: −782

∞ 2 17 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 23 3 5 7 11 13 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} 0 782  1^{2} 3_{+} 2 2 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23  2  2 2  2
C_{2} 24  2 2  2 2
2. 1_{k} 3_{+} 1_{−} 1_{k} -1 13 -17 1^{2} 3_{+} 2 2 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 3 2 3 2 2 3  2
S_{3} 2 2 3 3 2 2 3

Discriminant class: −391

∞ 2 17 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 23 3 5 7 11 13 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
3. 1_{k} 0_{+} 1_{−} 1_{k} 0 391  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 2  2 2 2
C_{2} 14  2 2  2  2

Discriminant class: −46

∞ 2 17 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 23  3 5 7 11 13 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 2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 2  2  2  2
C_{2} 4  2
5. 1_{k} 3_{+} 2_{+} 1_{i} -1 6 -46 1^{2} 3_{+} 2 2 1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 2  2 3 2 3 2 3
S_{3}  3  3 3 3 2 3

Discriminant class: −34

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

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

Discriminant class: −17

∞ 2 17 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 23 3 5 7 11 13 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} 2_{i} 1_{+} 0_{+} 0 17  1^{2} 2_{i} −1 −1 1^{2} 1_{+} 17 17  2  2 2
C_{2} 4  2 2 2 2  2 2 2

Discriminant class: −2

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

Discriminant class: −1

∞ 2 17 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17 Over p = 23 3 5 7 11 13 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
12. 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
13. 1_{k} 2_{i} 0_{+} 2_{+} -1 8 -6 1^{2} 2_{i} −1 −1  1^{3} 2_{+} ∗  2 3 2 2 3 2 3 2
S_{3} 2  3 2 2 3 2 3 2

Discriminant class: 2

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

Discriminant class: 17

∞ 2 17 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 23 3 5 7 11 13 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
15. 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: 23

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

Discriminant class: 34

∞ 2 17 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 23 3 5 7 11 13 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_{+} 3_{+} 1_{+} 0_{+} 0 -34  1^{2} 3_{+} 2 2 1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2  2 2  2
C_{2} 2  2 2  2 2  2

Discriminant class: 46

∞ 2 17 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 23 3 5 7 11 13 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
18. 0_{+} 3_{i} 0_{+} 1_{k} 0 -46  1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗ 1^{2} 1_{k} 23 23  2 2 2 2 2
C_{2}  2 2  2
19. 0_{+} 3_{i} 2_{+} 1_{k} -1 -62 -114 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{2} 1_{k} 23 23  3 3 2 2 2 2 2
S_{3}  3 3 2 2 3 3  2

Discriminant class: 391

∞ 2 17 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 23  3 5 7 11 13 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} 1_{−} 1_{i} 0 -391  1^{2} 2_{i} −1 −1 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{i} 23∗ 23∗  2 2  2
C_{2} 2  2  2 2 2

Discriminant class: 782

∞ 2 17 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 23  3 5 7 11 13 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
21. 0_{+} 3_{i} 1_{−} 1_{i} 0 -782  1^{2} 3_{i} −2 −2 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{i} 23∗ 23∗ 2 2 2  2 2
C_{2} 2  2 2 2 2  2 2