Low Degree Fields Unramified Outside of {∞, 17, 19, 23}

Discriminant class: −391

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

Discriminant class: −323

∞ 17 19 23 a_{1} a_{2} a_{3}  Over p = 17  Over p = 19  Over p = 23 2 3 5 7 11 13 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
2. 1_{k} 1_{+} 1_{i} 0_{+} 0 323  1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗ 2 0_{+} ∗ ∗ 2  2 2 2 2
C_{2} 4  2 2 2 2
3. 1_{k} 1_{+} 1_{i} 2_{+} 0 92 -207 1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗ 2 2 2 2 2 3 3
S_{3} 2  3 3 3 3 2 2 2 2

Discriminant class: −23

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

Discriminant class: −19

∞ 17 19 23 a_{1} a_{2} a_{3} Over p = 17  Over p = 19  Over p = 23 2 3 5 7 11 13 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
6. 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

Discriminant class: 1

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

Discriminant class: 17

∞ 17 19 23 a_{1} a_{2}  a_{3}  Over p = 17  Over p = 19 Over p = 23 2 3 5 7 11 13 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_{+} 1_{+} 0_{+} 0_{+} 1 -4  1^{2} 1_{+} 17 17  2 0_{+} ∗ ∗  2 2 2 2  2 2
C_{2}  2 2  2
9. 0_{+} 1_{+} 2_{+} 2_{+} 0 -437 -3059 1^{2} 1_{+} 17 17 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  3 2 2 2 2 3 2 2
S_{3} 3  2 2  3 3 3 2 3

Discriminant class: 437

∞ 17 19 23 a_{1} a_{2} a_{3} Over p = 17  Over p = 19  Over p = 23  2 3 5 7 11 13 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_{+} 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: 7429

∞ 17 19 23 a_{1}  a_{2} a_{3}  Over p = 17  Over p = 19  Over p = 23 2 3 5 7 11 13 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_{−} 1_{k} 1_{k} 0 -7429  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 19 19 1^{2} 1_{k} 23 23 2  2
C_{2} 2  2  2  2