Low Degree Fields Unramified Outside of {∞, 5, 23, 29}

Discriminant class: −3335

∞ 5 23 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 23 Over p = 29 2 3 7 11 13 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_{k} 1_{+} 0 3335 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 23 23 1^{2} 1_{+} 29 29 2 2 2
C_{2} 64  2 2 2

Discriminant class: −667

∞ 5 23 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 23  Over p = 29 2 3 7 11 13 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  2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2  2
C_{2} 4  2  2 2  2
3. 1_{k} 2_{+} 1_{i} 1_{+} -1 7 72 1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{+} 29 29 2 2 2 3 3 3 3 2
S_{3} 2 3 2 2 3 2

Discriminant class: −115

∞ 5 23 29 a_{1} a_{2} a_{3} Over p = 5 Over p = 23 Over p = 29 2 3 7 11 13 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_{k} 0_{+} 0 115  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 23 23  2 2  2 2  2
C_{2} 2  2  2

Discriminant class: −23

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

Discriminant class: 5

∞ 5 23 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 23 Over p = 29 2 3 7 11 13 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_{+} 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 23 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 23  Over p = 29 2 3 7 11 13 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_{+} 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 23 29 a_{1} a_{2} a_{3} Over p = 5  Over p = 23  Over p = 29 2 3 7 11 13 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_{+} 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