Low Degree Fields Unramified Outside of {∞, 7, 11, 29}

Discriminant class: −319

∞ 7 11 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 29  2 3 5 13 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} 0_{+} 1_{k} 1_{−} 0 319  2 0_{+} ∗ ∗ 1^{2} 1_{k} 11 11 1^{2} 1_{−} 29∗ 29∗  2  2  2
C_{2} 10  2  2

Discriminant class: −203

∞ 7 11 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 11 Over p = 29 2 3 5 13 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
2. 1_{k} 1_{i} 0_{+} 1_{+} 0 203  1^{2} 1_{i} 7∗ 7∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 2  2 2
C_{2} 4  2  2  2
3. 1_{k} 1_{i} 2_{+} 1_{+} -1 37 -42 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  1^{2} 1_{+} 29 29 2  2 2 3 3 3 3
S_{3}  2 3 2 3 3 2 3 3

Discriminant class: −11

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

Discriminant class: −7

∞ 7 11 29 a_{1} a_{2} a_{3} Over p = 7 Over p = 11 Over p = 29 2 3 5 13 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 2  1^{2} 1_{i} 7∗ 7∗  2 2 2 2 2  2
C_{2}  2  2  2 2

Discriminant class: 1

∞ 7 11 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 11 Over p = 29 2 3 5 13 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
7. 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

Discriminant class: 29

∞ 7 11 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 29 2 3 5 13 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_{+} 0_{+} 1_{+} 0 -29  2 0_{+} ∗ ∗ 1^{2} 1_{+} 29 29 2 2  2 2  2
C_{2}  2 2 2 2  2
9. 0_{+} 2_{+} 2_{+} 1_{+} -1 -51 134 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  1^{2} 1_{+} 29 29 2 2 3 3 2 2 3 2
S_{3} 3  2 2 2 2 3 3 2

Discriminant class: 77

∞ 7 11 29 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 29 2 3 5 13 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
10. 0_{+} 1_{k} 1_{i} 0_{+} 0 -77  1^{2} 1_{k} 7 7 1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 2 2 2  2
C_{2}  2 2  2

Discriminant class: 2233

∞ 7 11 29 a_{1}  a_{2} a_{3} Over p = 7  Over p = 11  Over p = 29  2 3 5 13 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_{+} 1_{k} 1_{k} 1_{−} 0 -2233  1^{2} 1_{k} 7 7 1^{2} 1_{k} 11 11 1^{2} 1_{−} 29∗ 29∗  2  2 2
C_{2} 6  2 2  2 2
12. 0_{+} 1_{k} 1_{k} 1_{−} -1  -8 1 1^{2} 1_{k} 7 7 1^{2} 1_{k} 11 11 1^{2} 1_{−} 29∗ 29∗ 3 3 2 3 2 2 3 3
S_{3}  2 2 3  3 2 2