Low Degree Fields Unramified Outside of {∞, 13, 19, 23}

Discriminant class: −299

∞ 13 19 23 a_{1} a_{2} a_{3}  Over p = 13  Over p = 19  Over p = 23  2 3 5 7 11 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_{+} 0_{+} 1_{i} 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
2. 1_{k} 1_{+} 2_{+} 1_{i} -1 -44 292 1^{2} 1_{+} 13 13 1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 2 3 3 3 3 2 3 2
S_{3} 6  3 2 2 2 2 2 2 3

Discriminant class: −247

∞ 13 19 23 a_{1} a_{2} a_{3}  Over p = 13  Over p = 19  Over p = 23 2 3 5 7 11 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} 1_{−} 1_{k} 0_{+} 0 247  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{k} 19 19  2 2 2 2  2
C_{2} 6  2 2
4. 1_{k} 1_{−} 1_{k} 0_{+} 0 1 -3 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{k} 19 19 3 0_{+} 1  3 2 2 2 2 3 2 3
S_{3}  3 3 3 2 2 3 3 3

Discriminant class: −23

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

Discriminant class: −19

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

Discriminant class: 1

∞ 13 19 23 a_{1} a_{2} a_{3} Over p = 13 Over p = 19 Over p = 23 2 3 5 7 11 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 -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
9. 0_{+} 0_{+} 2_{+} 0_{+} -1 -6 7 3 0_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3 3 3  3 3
C_{3}  3 3 3 3 3 3 3
10. 0_{+} 2_{+} 2_{+} 0_{+} -1 -82 64 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3 3
C_{3} 3  3  3 3 3 3  3

Discriminant class: 1 (continued)

∞ 13 19 23 a_{1} a_{2} a_{3} Over p = 13 Over p = 19 Over p = 23 2 3 5 7 11 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 -82 311 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3
C_{3} 3  3 3  3 3  3

Discriminant class: 13

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

Discriminant class: 437

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

Discriminant class: 5681

∞ 13 19 23 a_{1}  a_{2} a_{3}  Over p = 13  Over p = 19  Over p = 23  2 3 5 7 11 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_{+} 1_{−} 1_{i} 1_{i} 0 -5681  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗  2  2 2
C_{2} 2  2  2 2  2 2