Low Degree Fields Unramified Outside of {∞, 5, 17, 19}

Discriminant class: −1615

∞ 5 17 19 a_{1} a_{2} a_{3}  Over p = 5  Over p = 17  Over p = 19  2 3 7 11 13 23 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 1615  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{i} 19∗ 19∗  2  2
C_{2} 24  2  2 2  2 2
2. 1_{k} 1_{−} 1_{−} 1_{i} 0  7 -3 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{i} 19∗ 19∗ 3 2 3 2 3 3  3
S_{3}  2 3 2 2  2 2

Discriminant class: −323

∞ 5 17 19 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 19  2 3 7 11 13 23 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_{i} 0 323  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗ 2  2 2 2 2
C_{2} 4  2 2 2 2
4. 1_{k} 2_{+} 1_{+} 1_{i} -1 -18 52 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗ 2 3 2 2 2 2 3
S_{3}  3 3 3 3 2 2 2 2

Discriminant class: −95

∞ 5 17 19 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 19  2 3 7 11 13 23 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} 1_{+} 0_{+} 1_{i} 0 95  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 1^{2} 1_{i} 19∗ 19∗  2  2 2 2
C_{2} 8  2 2 2  2
6. 1_{k} 1_{+} 2_{+} 1_{i} 0 17 -17 1^{2} 1_{+} 5 5 1^{3} 2_{+} ∗  1^{2} 1_{i} 19∗ 19∗ 3 3 2 3 3 2 2 2
S_{3} 4  3 2 2 2 3 2

Discriminant class: −19

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

Discriminant class: 1

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

Discriminant class: 5

∞ 5 17 19 a_{1} a_{2} a_{3} Over p = 5  Over p = 17 Over p = 19 2 3 7 11 13 23 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
9. 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
10. 0_{+} 1_{+} 2_{+} 2_{+} -1 -215 1280 1^{2} 1_{+} 5 5 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 2 2 3 2 2 3 3
S_{3} 3  2 3 2 2 2 3  2

Discriminant class: 17

∞ 5 17 19 a_{1} a_{2} a_{3} Over p = 5  Over p = 17  Over p = 19 2 3 7 11 13 23 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_{+} 0_{+} 1_{+} 0_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17  2 2 2  2 2 2
C_{2}  2 2  2
12. 0_{+} 2_{+} 1_{+} 2_{+} 0 -95 -190 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 1^{3} 2_{+} 1  2 2 2 3 2 2 2
S_{3} 3  2 2 3 3 3 3 2 3

Discriminant class: 85

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