Low Degree Fields Unramified Outside of {∞, 23, 53}

Discriminant class: −1219

∞ 23 53 a_{1} a_{2} a_{3}  Over p = 23  Over p = 53  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 59 61
1. 1_{k} 1_{k} 1_{−} 0 1219  1^{2} 1_{k} 23 23 1^{2} 1_{−} 53∗ 53∗ 2 2  2 2  2
C_{2} 6  2 2 2 2
2. 1_{k} 1_{k} 1_{−} 0  -8 -11 1^{2} 1_{k} 23 23 1^{2} 1_{−} 53∗ 53∗ 2 2 3 2 2 3 2
S_{3}  3 2 2 2 2 3 3 3

Discriminant class: −23

∞ 23 53 a_{1} a_{2} a_{3}  Over p = 23  Over p = 53 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 43 47 59 61
3. 1_{k} 1_{i} 0_{+} 0 23  1^{2} 1_{i} 23∗ 23∗ 2 0_{+} ∗ ∗  2 2 2  2 2
C_{2} 3  2  2  2
4. 1_{k} 1_{i} 0_{+} -1 0 1 1^{2} 1_{i} 23∗ 23∗ 2 0_{+} ∗ ∗ 3 3 2 2 2 3 2 2
S_{3} 3 3 2 3 2 3 2

Discriminant class: 53

∞ 23 53 a_{1} a_{2} a_{3} Over p = 23  Over p = 53 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 59 61
5. 0_{+} 0_{+} 1_{+} 0 -53  2 0_{+} ∗ ∗ 1^{2} 1_{+} 53 53 2 2 2  2
C_{2}  2  2  2
6. 0_{+} 2_{+} 1_{+} -1 -38 -52 1^{3} 2_{+} ∗  1^{2} 1_{+} 53 53 2 2 2 3 3  3 2
S_{3}  3 2  2 3 3 3 2