Low Degree Fields Unramified Outside of {∞, 13, 23, 29}

Discriminant class: −8671

∞ 13 23 29 a_{1} a_{2} a_{3}  Over p = 13  Over p = 23  Over p = 29 2 3 5 7 11 17 19 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_{i} 1_{+} 0 8671  1^{2} 1_{+} 13 13 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29  2  2  2
C_{2} 64  2  2 2

Discriminant class: −667

∞ 13 23 29 a_{1} a_{2} a_{3} Over p = 13  Over p = 23  Over p = 29 2 3 5 7 11 17 19 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_{+} 0 667  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2 2  2
C_{2} 4  2  2 2  2
3. 1_{k} 2_{+} 1_{i} 1_{+} -1 22 116 1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2 2 3 3 3 2
S_{3} 6 2 2 2 3 3 2

Discriminant class: −299

∞ 13 23 29 a_{1} a_{2} a_{3}  Over p = 13  Over p = 23  Over p = 29 2 3 5 7 11 17 19 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_{i} 0_{+} 0 299  1^{2} 1_{+} 13 13 1^{2} 1_{i} 23∗ 23∗  2  2  2
C_{2} 8  2 2 2 2 2 2

Discriminant class: −23

∞ 13 23 29 a_{1} a_{2} a_{3} Over p = 13  Over p = 23  Over p = 29 2 3 5 7 11 17 19 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_{+} 0 23  1^{2} 1_{i} 23∗ 23∗  2 2 2 2 2
C_{2} 3  2  2  2  2 2
6. 1_{k} 0_{+} 1_{i} 0_{+} -1 0 1 3 0_{+} 1  1^{2} 1_{i} 23∗ 23∗ 3 0_{+} 1  3 3 2 2 2 2 2 3
S_{3}  2 3 2 3 2  2 2

Discriminant class: 1

∞ 13 23 29 a_{1} a_{2} a_{3} Over p = 13 Over p = 23 Over p = 29 2 3 5 7 11 17 19 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 -4 -1 1^{3} 2_{+} 1  3 0_{+} 1  3 0_{+} 1  3 3  3 3 3 3
C_{3}  3 3 3  3 3 3

Discriminant class: 13

∞ 13 23 29 a_{1} a_{2} a_{3}  Over p = 13  Over p = 23 Over p = 29 2 3 5 7 11 17 19 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 -3  1^{2} 1_{+} 13 13  2  2 2 2  2 2
C_{2}  2 2  2  2  2

Discriminant class: 29

∞ 13 23 29 a_{1} a_{2} a_{3} Over p = 13 Over p = 23  Over p = 29 2 3 5 7 11 17 19 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: 377

∞ 13 23 29 a_{1} a_{2} a_{3}  Over p = 13  Over p = 23  Over p = 29 2 3 5 7 11 17 19 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 -377  1^{2} 1_{+} 13 13  1^{2} 1_{+} 29 29  2 2 2  2
C_{2} 2  2  2 2 2