Low Degree Fields Unramified Outside of {∞, 53, 59}

Discriminant class: −3127

∞ 53 59 a_{1} a_{2} a_{3}  Over p = 53  Over p = 59  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 61
1. 1_{k} 1_{+} 1_{i} 0 3127  1^{2} 1_{+} 53 53 1^{2} 1_{i} 59∗ 59∗  2 2  2 2  2
C_{2} 24  2 2 2 2
2. 1_{k} 1_{+} 1_{i} -1 -16 33 1^{2} 1_{+} 53 53 1^{2} 1_{i} 59∗ 59∗ 3 2 2 3 2 2  2
S_{3}  3 3 3 2 2 2 2

Discriminant class: −59

∞ 53 59 a_{1} a_{2} a_{3} Over p = 53  Over p = 59  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 61
3. 1_{k} 0_{+} 1_{i} 0 59  1^{2} 1_{i} 59∗ 59∗ 2  2 2
C_{2} 3  2  2 2  2 2 2
4. 1_{k} 0_{+} 1_{i} 0 2 -1 3 0_{+} 1  1^{2} 1_{i} 59∗ 59∗ 2 3 3 3 2 2  3
S_{3}  2 3 2 2 3 2 2 2

Discriminant class: 53

∞ 53 59 a_{1} a_{2} a_{3} Over p = 53 Over p = 59 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 61
5. 0_{+} 1_{+} 0_{+} 0 -53  1^{2} 1_{+} 53 53  2 2 2  2
C_{2}  2  2  2  2