Low Degree Fields Unramified Outside of {∞, 5, 13, 29}

Discriminant class: 1

∞ 5 13 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 13 Over p = 29 2 3 7 11 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. 0_{+} 0_{+} 2_{+} 0_{+} -1 -4 -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: 5

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

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

Discriminant class: 29

∞ 5 13 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 13 Over p = 29 2 3 7 11 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. 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: 65

∞ 5 13 29 a_{1} a_{2} a_{3}  Over p = 5  Over p = 13  Over p = 29 2 3 7 11 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. 0_{+} 1_{−} 1_{−} 0_{+} 0 -65  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 13∗ 13∗  2  2 2 2 2 2
C_{2} 2  2 2  2 2

Discriminant class: 145

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

Discriminant class: 377

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

Discriminant class: 1885

∞ 5 13 29 a_{1}  a_{2} a_{3}  Over p = 5  Over p = 13  Over p = 29 2 3 7 11 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_{−} 1_{−} 1_{+} 0 -1885  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{+} 29 29 2  2
C_{2} 4  2  2 2 2 2