Low Degree Fields Unramified Outside of {∞, 11, 19, 23}

Discriminant class: −4807

∞ 11 19 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 19  Over p = 23  2 3 5 7 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 4807  1^{2} 1_{k} 11 11 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{i} 23∗ 23∗  2 2  2
C_{2} 40  2

Discriminant class: −23

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

∞ 11 19 23 a_{1} a_{2} a_{3} Over p = 11  Over p = 19  Over p = 23 2 3 5 7 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
4. 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: −11

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

Discriminant class: 1

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

Discriminant class: 209

∞ 11 19 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 19  Over p = 23 2 3 5 7 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. 0_{+} 1_{i} 1_{k} 0_{+} 0 -209  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{k} 19 19  2  2  2  2
C_{2}  2  2  2 2 2 2

Discriminant class: 253

∞ 11 19 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 19  Over p = 23  2 3 5 7 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_{+} 1_{k} 0_{+} 1_{i} 0 -253  1^{2} 1_{k} 11 11  1^{2} 1_{i} 23∗ 23∗ 2  2  2  2
C_{2}  2 2  2  2
9. 0_{+} 1_{k} 2_{+} 1_{i} -1 -63 -164 1^{2} 1_{k} 11 11 1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 2 3 2 3 2 3 2 3
S_{3} 3  2 2 3 3 2  3 2

Discriminant class: 437

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