Low Degree Fields Unramified Outside of {∞, 53, 71}

Discriminant class: −3763

∞ 53 71 a_{1} a_{2} a_{3}  Over p = 53  Over p = 71 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 59
1. 1_{k} 1_{−} 1_{k} 0 3763  1^{2} 1_{−} 53∗ 53∗ 1^{2} 1_{k} 71 71 2 2 2 2 2 2 2 2
C_{2} 6  2 2
2. 1_{k} 1_{−} 1_{k} 0  -5 -24 1^{2} 1_{−} 53∗ 53∗ 1^{2} 1_{k} 71 71 2 2 2 2 2 2 2 2
S_{3} 3 3 3 3 3 2 2

Discriminant class: −71

∞ 53 71 a_{1} a_{2} a_{3} Over p = 53  Over p = 71  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 29 31 37 41 43 47 59
3. 1_{k} 0_{+} 1_{i} 0 71  2 0_{+} ∗ ∗ 1^{2} 1_{i} 71∗ 71∗  2 2 2 2
C_{2} 7  2  2  2  2 2
4. 1_{k} 2_{+} 1_{i} 0 53 -583 1^{3} 2_{+} ∗  1^{2} 1_{i} 71∗ 71∗ 3 3 3 2 2 2 2 3
S_{3}  2 3 2 3 2 3 2 2

Discriminant class: 53

∞ 53 71 a_{1} a_{2} a_{3} Over p = 53 Over p = 71 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 59
5. 0_{+} 1_{+} 0_{+} 0 -53  1^{2} 1_{+} 53 53 2 0_{+} ∗ ∗ 2 2 2  2
C_{2}  2  2  2
6. 0_{+} 1_{+} 2_{+} -1 -47 92 1^{2} 1_{+} 53 53 1^{3} 2_{+} ∗  2 2 2 3 3 3 3 2
S_{3}  2  2 3 2  3