Low Degree Fields Unramified Outside of {∞, 5, 17, 23}

Discriminant class: −1955

∞ 5 17 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 23  2 3 7 11 13 19 29 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_{+} 1_{i} 0 1955  1^{2} 1_{+} 5 5 1^{2} 1_{+} 17 17 1^{2} 1_{i} 23∗ 23∗ 2  2  2 2 2 2
C_{2} 12  2 2  2
2. 1_{k} 1_{+} 1_{+} 1_{i} -1  -5 -8 1^{2} 1_{+} 5 5 1^{2} 1_{+} 17 17 1^{2} 1_{i} 23∗ 23∗ 2 3 2 3 2 2 2 2
S_{3}  2 2 3 2 3 3 3

Discriminant class: −391

∞ 5 17 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 23 2 3 7 11 13 19 29 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. 1_{k} 0_{+} 1_{−} 1_{k} 0 391  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23  2  2 2 2
C_{2} 14  2 2  2  2

Discriminant class: −115

∞ 5 17 23 a_{1} a_{2} a_{3} Over p = 5 Over p = 17 Over p = 23 2 3 7 11 13 19 29 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_{−} 0_{+} 1_{k} 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 17 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 23  2 3 7 11 13 19 29 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_{+} 0_{+} 1_{i} 0 23  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗  2 2  2
C_{2} 3  2  2  2  2 2
6. 1_{k} 0_{+} 0_{+} 1_{i} -1 0  1 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 3 2 3 3
S_{3}  2 3 2 3 2  2 2
7. 1_{k} 2_{+} 2_{+} 1_{i} 0 -85 -340 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗  3 2 2 3 2 3 3
S_{3} 3  2 3 2  2 3 2 2
8. 1_{k} 2_{+} 2_{+} 1_{i} -1 -28 107 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 3 2 3
S_{3} 3  2  2 3 2 3 2 2
9. 1_{k} 2_{+} 2_{+} 1_{i} -1 -28 -233 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3  2 2  2  3
S_{3} 3  2 3 2 3 2 3 2 2

Discriminant class: 5

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

Discriminant class: 5 (continued)

∞ 5 17 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 17 Over p = 23 2 3 7 11 13 19 29 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_{+} 2_{+} 2_{+} -1 -130 -420 1^{2} 1_{+} 5 5 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 2  2 3 3 3
S_{3}  2  2 2 2 3  2

Discriminant class: 17

∞ 5 17 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 23 2 3 7 11 13 19 29 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
12. 0_{+} 0_{+} 1_{+} 0_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2 2 2  2 2
C_{2}  2 2  2
13. 0_{+} 2_{+} 1_{+} 2_{+} -1 -38 17 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 1^{3} 2_{+} ∗  3 2 2 2 3  2 2
S_{3}  2 2 3  3 2 3

Discriminant class: 85

∞ 5 17 23 a_{1} a_{2} a_{3}  Over p = 5  Over p = 17  Over p = 23 2 3 7 11 13 19 29 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
14. 0_{+} 1_{−} 1_{−} 0_{+} 0 -85  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 17∗ 17∗  2  2 2  2 2
C_{2} 2  2 2 2 2  2 2