Low Degree Fields Unramified Outside of {∞, 11, 13, 29}

Discriminant class: −4147

∞ 11 13 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 29  2 3 5 7 17 19 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_{i} 1_{−} 1_{−} 0 4147  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 2  2
C_{2} 12  2  2  2
2. 1_{k} 1_{i} 1_{−} 1_{−} -1  -1 -12 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 29∗ 29∗ 2 2 2 3 3 2 3 3
S_{3} 3 2 3 3 2 3 2

Discriminant class: −319

∞ 11 13 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 29  2 3 5 7 17 19 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 2 0_{+} ∗ ∗ 1^{2} 1_{−} 29∗ 29∗  2  2  2
C_{2} 10  2  2

Discriminant class: −143

∞ 11 13 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 29 2 3 5 7 17 19 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
4. 1_{k} 1_{k} 1_{−} 0_{+} 0 143  1^{2} 1_{k} 11 11 1^{2} 1_{−} 13∗ 13∗ 2 0_{+} ∗ ∗  2  2  2
C_{2} 10  2  2 2  2 2 2
5. 1_{k} 1_{k} 1_{−} 2_{+} 0 29 -29 1^{2} 1_{k} 11 11 1^{2} 1_{−} 13∗ 13∗ 1^{3} 2_{+} ∗  3 3 2 3 2  2
S_{3} 8  2 3 2 2 3 2 2 2

Discriminant class: −11

∞ 11 13 29 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13 Over p = 29 2 3 5 7 17 19 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
6. 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
7. 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 13 29 a_{1} a_{2} a_{3} Over p = 11 Over p = 13 Over p = 29 2 3 5 7 17 19 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_{+} 0_{+} 2_{+} 0_{+} -1 -4 -1 3 0_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3 3  3 3 3 3
C_{3}  3 3 3  3 3 3

Discriminant class: 13

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

Discriminant class: 29

∞ 11 13 29 a_{1} a_{2} a_{3} Over p = 11 Over p = 13  Over p = 29 2 3 5 7 17 19 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_{+} 0_{+} 0_{+} 1_{+} 0 -29  2 0_{+} ∗ ∗  1^{2} 1_{+} 29 29 2 2  2 2  2
C_{2}  2 2 2 2  2
12. 0_{+} 2_{+} 2_{+} 1_{+} 0 -143 -286 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{+} 29 29 2 2 3 3 2 2 3 2
S_{3} 3  2 2 2 2 3  2 3

Discriminant class: 377

∞ 11 13 29 a_{1} a_{2} a_{3} Over p = 11  Over p = 13  Over p = 29 2 3 5 7 17 19 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
13. 0_{+} 0_{+} 1_{+} 1_{+} 0 -377  1^{2} 1_{+} 13 13 1^{2} 1_{+} 29 29  2 2 2 2
C_{2} 2  2  2 2 2