Low Degree Fields Unramified Outside of {∞, 7, 19, 29}

Discriminant class: −551

∞ 7 19 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 19  Over p = 29  2 3 5 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} 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
2. 1_{k} 2_{+} 1_{k} 1_{−} -1 -2 64 1^{3} 2_{+} 1 1^{2} 1_{k} 19 19 1^{2} 1_{−} 29∗ 29∗ 3 3 2 2 2 3
S_{3} 3  3 3 2 2 2 2 2 2

Discriminant class: −203

∞ 7 19 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 19 Over p = 29 2 3 5 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_{i} 0_{+} 1_{+} 0 203  1^{2} 1_{i} 7∗ 7∗  1^{2} 1_{+} 29 29 2  2 2 2
C_{2} 4  2  2  2
4. 1_{k} 1_{i} 2_{+} 1_{+} 0 -19 -418 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} 1  1^{2} 1_{+} 29 29 2 3 2 2 2 3 3 3
S_{3} 3 2 3 2 3 3 2 3

Discriminant class: −19

∞ 7 19 29 a_{1} a_{2}  a_{3} Over p = 7  Over p = 19  Over p = 29 2 3 5 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} 2_{+} 1_{i} 0_{+} -1  5  -6 1^{3} 2_{+} 1  1^{2} 1_{i} 19∗ 19∗ 2 0_{+} ∗ ∗ 2 2 3 3 2  3 2
S_{3} 3  2 2 3 3 2 2 3 2
7. 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
8. 1_{k} 2_{+} 1_{i} 2_{+} -1 68 624 1^{3} 2_{+} 1  1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2 3 3 2  3 2
S_{3} 3  2 2  2 2  2
9. 1_{k} 2_{+} 1_{i} 2_{+} -1 -135 -1000 1^{3} 2_{+} 1  1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 2  3 2  3 2
S_{3} 9  2 2 3 3 2 2 3 2

Discriminant class: −7

∞ 7 19 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 19 Over p = 29 2 3 5 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. 1_{k} 1_{i} 0_{+} 0_{+} 1 2  1^{2} 1_{i} 7∗ 7∗ 2 0_{+} ∗ ∗  2 2  2 2  2
C_{2}  2  2  2 2

Discriminant class: 1

∞ 7 19 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 19 Over p = 29 2 3 5 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
11. 0_{+} 2_{+} 0_{+} 0_{+} -1 -2 1 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3  3 3 3
C_{3}  3  3 3 3 3 3
12. 0_{+} 0_{+} 2_{+} 0_{+} -1 -6 7  1^{3} 2_{+} 1  3 0_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3 3 3 3 3
13. 0_{+} 2_{+} 2_{+} 0_{+} -1 -44 -69 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3  3 3 3  3
C_{3} 3  3 3 3  3  3
14. 0_{+} 2_{+} 2_{+} 0_{+} 1 -44 -64 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3  3 3 3 3 3
C_{3} 3  3 3 3 3  3 3

Discriminant class: 29

∞ 7 19 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 19  Over p = 29 2 3 5 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
15. 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: 133

∞ 7 19 29 a_{1} a_{2} a_{3}  Over p = 7  Over p = 19  Over p = 29 2 3 5 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
16. 0_{+} 1_{i} 1_{k} 0_{+} 0 -133  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 19 19 2 0_{+} ∗ ∗ 2  2  2
C_{2}  2  2 2  2 2

Discriminant class: 3857

∞ 7 19 29 a_{1}  a_{2} a_{3}  Over p = 7  Over p = 19  Over p = 29  2 3 5 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
17. 0_{+} 1_{i} 1_{i} 1_{−} 0 -3857  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{−} 29∗ 29∗  2 2 2  2
C_{2} 2  2 2  2  2