Low Degree Fields Unramified Outside of {∞, 19, 23, 29}

Discriminant class: −667

∞ 19 23 29 a_{1} a_{2} a_{3} Over p = 19  Over p = 23  Over p = 29 2 3 5 7 11 13 17 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} 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
2. 1_{k} 2_{+} 1_{i} 1_{+} -1 -63 710 1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2 2  3 3 2
S_{3} 3  3 2 3 2 2 3 3 2

Discriminant class: −551

∞ 19 23 29 a_{1} a_{2} a_{3}  Over p = 19  Over p = 23  Over p = 29  2 3 5 7 11 13 17 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_{k} 0_{+} 1_{−} 0 551  1^{2} 1_{k} 19 19  1^{2} 1_{−} 29∗ 29∗  2 2 2
C_{2} 26  2 2 2 2 2 2

Discriminant class: −23

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

∞ 19 23 29 a_{1} a_{2} a_{3}  Over p = 19  Over p = 23 Over p = 29 2 3 5 7 11 13 17 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} 1_{i} 0_{+} 0_{+} -1 5  1^{2} 1_{i} 19∗ 19∗  2 0_{+} ∗ ∗ 2 2  2  2
C_{2}  2 2  2 2  2
7. 1_{k} 1_{i} 0_{+} 2_{+} -1 10 44 1^{2} 1_{i} 19∗ 19∗  1^{3} 2_{+} ∗  2 2 3 3  2  2
S_{3}  2 2 3 3 2 2 3 2

Discriminant class: 1

∞ 19 23 29 a_{1} a_{2} a_{3} Over p = 19 Over p = 23 Over p = 29 2 3 5 7 11 13 17 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. 0_{+} 2_{+} 0_{+} 0_{+} -1 -6 7 1^{3} 2_{+} 1 3 0_{+} 1 3 0_{+} 1 3 3 3 3 3
C_{3}  3 3 3 3 3 3 3

Discriminant class: 29

∞ 19 23 29 a_{1} a_{2} a_{3} Over p = 19 Over p = 23  Over p = 29 2 3 5 7 11 13 17 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: 437

∞ 19 23 29 a_{1} a_{2} a_{3}  Over p = 19  Over p = 23  Over p = 29 2 3 5 7 11 13 17 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_{k} 1_{i} 0_{+} 0 -437  1^{2} 1_{k} 19 19 1^{2} 1_{i} 23∗ 23∗ 2 0_{+} ∗ ∗ 2 2 2 2 2 2 2 2
C_{2}  2 2  2 2

Discriminant class: 12673

∞ 19 23 29 a_{1}  a_{2} a_{3}  Over p = 19  Over p = 23  Over p = 29  2 3 5 7 11 13 17 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
11. 0_{+} 1_{i} 1_{i} 1_{−} 0 -12673  1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{−} 29∗ 29∗  2 2  2
C_{2} 2  2  2  2