Low Degree Fields Unramified Outside of {∞, 5, 53}

Discriminant class: 5

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

Discriminant class: 53

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

Discriminant class: 265

∞ 5 53 a_{1} a_{2} a_{3}  Over p = 5  Over p = 53  2 3 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 59 61
3. 0_{+} 1_{−} 1_{−} 0 -265  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 53∗ 53∗  2  2 2 2
C_{2} 2  2 2 2 2 2  2