Low Degree Fields Unramified Outside of {∞, 17, 23, 29}

Discriminant class: −11339

∞ 17 23 29 a_{1}  a_{2} a_{3}  Over p = 17  Over p = 23  Over p = 29  2 3 5 7 11 13 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} 1_{+} 1_{k} 1_{−} 0 11339  1^{2} 1_{+} 17 17 1^{2} 1_{k} 23 23 1^{2} 1_{−} 29∗ 29∗ 2  2
C_{2} 52  2  2 2  2 2

Discriminant class: −667

∞ 17 23 29 a_{1} a_{2} a_{3} Over p = 17  Over p = 23  Over p = 29 2 3 5 7 11 13 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  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2 2  2
C_{2} 4  2  2 2  2

Discriminant class: −391

∞ 17 23 29 a_{1} a_{2} a_{3}  Over p = 17  Over p = 23  Over p = 29 2 3 5 7 11 13 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
3. 1_{k} 1_{−} 1_{k} 0_{+} 0 391  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 2 0_{+} ∗ ∗  2  2 2
C_{2} 14  2 2  2  2
4. 1_{k} 1_{−} 1_{k} 2_{+} -1 68 -275 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 1^{3} 2_{+} ∗  3 2  3  3 2 2
S_{3}  3 2 2  2 3 3 2

Discriminant class: −23

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

Discriminant class: 17

∞ 17 23 29 a_{1} a_{2} a_{3} Over p = 17 Over p = 23 Over p = 29 2 3 5 7 11 13 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
7. 0_{+} 1_{+} 0_{+} 0_{+} 1 -4  1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗  2 2 2 2  2
C_{2}  2 2  2
8. 0_{+} 1_{+} 2_{+} 2_{+} -1 -222 -1087 1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  3 2 2 2 2 3 3 2
S_{3}  2 2 3  3  2 3

Discriminant class: 29

∞ 17 23 29 a_{1} a_{2} a_{3} Over p = 17 Over p = 23  Over p = 29 2 3 5 7 11 13 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
9. 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: 493

∞ 17 23 29 a_{1} a_{2} a_{3}  Over p = 17  Over p = 23  Over p = 29  2 3 5 7 11 13 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. 0_{+} 1_{−} 0_{+} 1_{−} 0 -493  1^{2} 1_{−} 17∗ 17∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 29∗ 29∗ 2  2 2  2
C_{2} 2  2 2
11. 0_{+} 1_{−} 2_{+} 1_{−} 0 -46 -69 1^{2} 1_{−} 17∗ 17∗ 1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 2  2 2 3 3 2 3
S_{3}  3  2 2 3 3 3 3