Low Degree Fields Unramified Outside of {∞, 5, 19, 29}

Discriminant class: −2755

∞ 5 19 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 19  Over p = 29  2 3 7 11 13 17 23 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 2755  1^{2} 1_{+} 5 5 1^{2} 1_{k} 19 19 1^{2} 1_{−} 29∗ 29∗ 2 2 2 2  2
C_{2} 8  2  2 2

Discriminant class: −551

∞ 5 19 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 19  Over p = 29  2 3 7 11 13 17 23 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_{−} 0 551  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: −95

∞ 5 19 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 19  Over p = 29 2 3 7 11 13 17 23 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_{i} 0_{+} 0 95  1^{2} 1_{+} 5 5 1^{2} 1_{i} 19∗ 19∗ 2 0_{+} ∗ ∗  2  2 2 2
C_{2} 8  2 2 2  2
4. 1_{k} 1_{+} 1_{i} 2_{+} -1 10 -275 1^{2} 1_{+} 5 5 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  3 3 2  3 2 2 2
S_{3}  3 2 2 2  2

Discriminant class: −19

∞ 5 19 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 19  Over p = 29 2 3 7 11 13 17 23 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_{+} -1 5  1^{2} 1_{i} 19∗ 19∗ 2 0_{+} ∗ ∗ 2 2  2  2
C_{2}  2 2  2 2  2
6. 1_{k} 0_{+} 1_{i} 2_{+} -1 10 44 3 0_{+} 1  1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2 3  2  2
S_{3}  2 2 3 3 2 2 3 2

Discriminant class: 1

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

Discriminant class: 5

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

Discriminant class: 29

∞ 5 19 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 19  Over p = 29 2 3 7 11 13 17 23 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: 145

∞ 5 19 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 19  Over p = 29 2 3 7 11 13 17 23 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 -145  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29  2 2 2  2 2
C_{2} 4  2  2  2 2