Low Degree Fields Unramified Outside of {∞, 2, 11, 17}

Discriminant class: −374

∞ 2 11 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 17  3 5 7 13 19 23 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_{i} 1_{−} 0 374  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 17∗ 17∗  2 2 2
C_{2} 28  2 2 2 2

Discriminant class: −187

∞ 2 11 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 17  3 5 7 13 19 23 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_{k} 1_{−} 0 187  2 0_{+} ∗ ∗ 1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2  2 2 2  2
C_{2} 2  2  2
3. 1_{k} 2_{+} 1_{k} 1_{−} -1 1 5 1^{3} 2_{+} ∗  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2 3 2 2 2 3 2
S_{3} 2 3 2 3 3 3 3

Discriminant class: −34

∞ 2 11 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 17 3 5 7 13 19 23 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_{i} 0_{+} 1_{+} 0 34  1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 2  2
C_{2} 4  2  2 2
5. 1_{k} 3_{i} 2_{+} 1_{+} -1 26 46 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 2 3 3 2 3  3
S_{3} 7  3 2 3 2 2 3 3

Discriminant class: −22

∞ 2 11 17 a_{1} a_{2} a_{3} Over p = 2 Over p = 11 Over p = 17 3 5 7 13 19 23 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_{−} 1_{k} 0_{+} 0 22  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 11 11 2 0_{+} ∗ ∗ 2 2 2
C_{2} 2 2 2 2 2 2
7. 1_{k} 3_{−} 1_{k} 2_{+} -1 6 90 1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 11 11 1^{3} 2_{+} ∗  2 2 2 3 3 3 3 3
S_{3} 2 2 3 2 2 2

Discriminant class: −17

∞ 2 11 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 17 3 5 7 13 19 23 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} 0_{+} 1_{+} 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: −11

∞ 2 11 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 17 3 5 7 13 19 23 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} 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
10. 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 3 2 3
S_{3} 3 2 2 3 2 3
11. 1_{k} 0_{+} 1_{i} 2_{+} -1 -11 22 2 0_{+} ∗ ∗ 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3 3 2 2 2 3 2
S_{3}  3 2 2 3  3 2
12. 1_{k} 2_{+} 1_{i} 2_{+} -1 23 5 1^{3} 2_{+} ∗  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3  2 2 2  2 3
S_{3} 3  3 2 2 3  3 2 3
13. 1_{k} 2_{+} 1_{i} 2_{+} -1 -11 -63 1^{3} 2_{+} ∗  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3 2 2 2 3 2 3
S_{3} 3  2 2 3  2 3

Discriminant class: −2

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

Discriminant class: −1

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

Discriminant class: 2

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

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

∞ 2 11 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 17 3 5 7 13 19 23 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_{+} 0_{+} 0_{+} 1_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 2 2 2  2 2 2
C_{2}  2 2  2
20. 0_{+} 0_{+} 2_{+} 1_{+} 0 -11 -11 3 0_{+} 1  1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 2 2 2 3 3 2 2 2
S_{3}  2 2 3 3  2 3

Discriminant class: 22

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

Discriminant class: 34

∞ 2 11 17 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 17 3 5 7 13 19 23 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_{+} 0_{+} 1_{+} 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: 187

∞ 2 11 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 17  3 5 7 13 19 23 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_{i} 1_{−} 0 -187  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 17∗ 17∗  2 2 2
C_{2} 2  2  2  2  2

Discriminant class: 374

∞ 2 11 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 17  3 5 7 13 19 23 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_{k} 1_{−} 0 -374  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2  2  2  2
C_{2} 2  2 2 2  2