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

Discriminant class: −23

∞ 19 23 a_{1} a_{2} a_{3} Over p = 19  Over p = 23  2 3 5 7 11 13 17 29
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
1. 1_{k} 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. 1_{k} 0_{+} 1_{i} -1 0 1 2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 2 3 2 3
S_{3} 3 2 3 2 3 2 2

Discriminant class: −19

∞ 19 23 a_{1} a_{2} a_{3}  Over p = 19  Over p = 23 2 3 5 7 11 13 17 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 1_{k} 1_{i} 0_{+} -1 5  1^{2} 1_{i} 19∗ 19∗  2 2  2  2
C_{2}  2 2 2  2 2

Discriminant class: 1

∞ 19 23 a_{1} a_{2} a_{3} Over p = 19 Over p = 23 2 3 5 7 11 13 17 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
4. 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

Discriminant class: 437

∞ 19 23 a_{1} a_{2} a_{3}  Over p = 19  Over p = 23  2 3 5 7 11 13 17 29
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
5. 0_{+} 1_{k} 1_{i} 0 -437  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 2