Low Degree Fields Unramified Outside of {∞, 5, 7, 29}

Discriminant class: −1015

∞ 5 7 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 29 2 3 11 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} 1_{−} 1_{k} 1_{+} 0 1015  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 1^{2} 1_{+} 29 29  2 2  2  2
C_{2} 16  2 2 2  2

Discriminant class: −203

∞ 5 7 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 29 2 3 11 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} 0_{+} 1_{i} 1_{+} 0 203  2 0_{+} ∗ ∗ 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 29 29 2  2 2
C_{2} 4  2  2  2
3. 1_{k} 2_{+} 1_{i} 1_{+} -1 2 -28 1^{3} 2_{+} ∗  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 29 29 2 3 2 2 3 3 3
S_{3} 2 2 3 2 3 3

Discriminant class: −35

∞ 5 7 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 Over p = 29 2 3 11 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} 1_{−} 1_{k} 0_{+} 0 35  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7  2  2 2 2
C_{2} 2  2 2 2  2 2 2 2

Discriminant class: −7

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

Discriminant class: 1

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

Discriminant class: 5

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

Discriminant class: 29

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

Discriminant class: 145

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