Low Degree Fields Unramified Outside of {∞, 11, 19, 29}

Discriminant class: −551

∞ 11 19 29 a_{1} a_{2} a_{3} Over p = 11  Over p = 19  Over p = 29  2 3 5 7 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  2 0_{+} ∗ ∗ 1^{2} 1_{k} 19 19 1^{2} 1_{−} 29∗ 29∗  2 2
C_{2} 26  2 2 2 2 2 2
2. 1_{k} 2_{+} 1_{k} 1_{−} -1 -40 -97 1^{3} 2_{+} ∗  1^{2} 1_{k} 19 19 1^{2} 1_{−} 29∗ 29∗ 3 3 3 3 2 2 3
S_{3}  3 3 2 2 2 2 2 2

Discriminant class: −319

∞ 11 19 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 19  Over p = 29  2 3 5 7 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_{k} 0_{+} 1_{−} 0 319  1^{2} 1_{k} 11 11  1^{2} 1_{−} 29∗ 29∗  2  2 2  2
C_{2} 10  2  2
4. 1_{k} 1_{k} 2_{+} 1_{−} 0 19 -57 1^{2} 1_{k} 11 11 1^{3} 2_{+} 1  1^{2} 1_{−} 29∗ 29∗ 3 2 3 2 2 3 3 2
S_{3} 6 2 2 3

Discriminant class: −19

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

∞ 11 19 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 19 Over p = 29 2 3 5 7 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. 1_{k} 1_{i} 0_{+} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 2  2 2 2
C_{2}  2 2  2
8. 1_{k} 1_{i} 0_{+} 2_{+} -1 -19 44 1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  2 3  2 2 2 3 3
S_{3} 2  3 2 2  3 3 2 3

Discriminant class: 1

∞ 11 19 29 a_{1} a_{2} a_{3} Over p = 11 Over p = 19 Over p = 29 2 3 5 7 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_{+} 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

Discriminant class: 29

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

Discriminant class: 209

∞ 11 19 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 19  Over p = 29 2 3 5 7 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_{+} 1_{i} 1_{k} 0_{+} 0 -209  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{k} 19 19  2  2  2  2
C_{2}  2  2  2 2 2 2

Discriminant class: 6061

∞ 11 19 29 a_{1}  a_{2} a_{3}  Over p = 11  Over p = 19  Over p = 29 2 3 5 7 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
12. 0_{+} 1_{k} 1_{i} 1_{+} 0 -6061  1^{2} 1_{k} 11 11 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{+} 29 29 2  2
C_{2} 2  2  2 2 2  2