Low Degree Fields Unramified Outside of {∞, 7, 19, 23}

Discriminant class: −3059

∞ 7 19 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 19  Over p = 23  2 3 5 11 13 17 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_{k} 1_{i} 1_{i} 0 3059  1^{2} 1_{k} 7 7 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗ 2  2  2
C_{2} 24  2 2
2. 1_{k} 1_{k} 1_{i} 1_{i} 0 11 -16 1^{2} 1_{k} 7 7 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗ 2 3 3 2 3 3 2
S_{3} 3 2 2 3 3 3

Discriminant class: −23

∞ 7 19 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 19  Over p = 23  2 3 5 11 13 17 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_{+} 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
4. 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

Discriminant class: −19

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

Discriminant class: −7

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

Discriminant class: 1

∞ 7 19 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 19 Over p = 23 2 3 5 11 13 17 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
8. 0_{+} 2_{+} 0_{+} 0_{+} -1 -2 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
9. 0_{+} 0_{+} 2_{+} 0_{+} -1 -6 7  1^{3} 2_{+} 1  3 0_{+} 1  3 3 3  3 3 3
C_{3}  3 3 3 3 3 3 3
10. 0_{+} 2_{+} 2_{+} 0_{+} -1 -44 -69 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3  3 3
C_{3} 3  3 3 3  3  3

Discriminant class: 1 (continued)

∞ 7 19 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 19 Over p = 23 2 3 5 11 13 17 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_{+} 2_{+} 2_{+} 0_{+} 1 -44 -64 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3  3 3 3 3 3
C_{3} 3  3 3 3 3  3 3

Discriminant class: 133

∞ 7 19 23 a_{1} a_{2} a_{3}  Over p = 7  Over p = 19  Over p = 23 2 3 5 11 13 17 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_{+} 1_{i} 1_{k} 0_{+} 0 -133  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 19 19  2  2  2 2
C_{2}  2  2 2  2 2

Discriminant class: 161

∞ 7 19 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 19  Over p = 23  2 3 5 11 13 17 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
13. 0_{+} 1_{k} 0_{+} 1_{i} 0 -161  1^{2} 1_{k} 7 7  1^{2} 1_{i} 23∗ 23∗  2  2 2  2
C_{2}  2 2 2 2 2 2  2

Discriminant class: 437

∞ 7 19 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 19  Over p = 23  2 3 5 11 13 17 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_{+} 0_{+} 1_{k} 1_{i} 0 -437  2 0_{+} ∗ ∗ 1^{2} 1_{k} 19 19 1^{2} 1_{i} 23∗ 23∗ 2 2 2 2 2 2 2 2
C_{2}  2 2  2 2