Low Degree Fields Unramified Outside of {∞, 59, 73}

Discriminant class: −4307

∞ 59 73 a_{1} a_{2} a_{3}  Over p = 59  Over p = 73  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 53
1. 1_{k} 1_{k} 1_{−} 0 4307  1^{2} 1_{k} 59 59 1^{2} 1_{−} 73∗ 73∗ 2  2 2  2
C_{2} 18  2 2  2  2
2. 1_{k} 1_{k} 1_{−} 0  -4 -13 1^{2} 1_{k} 59 59 1^{2} 1_{−} 73∗ 73∗ 2 3 2 2 3  2 3
S_{3}  2 2 3 2  3 3 2

Discriminant class: −59

∞ 59 73 a_{1} a_{2} a_{3}  Over p = 59  Over p = 73 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 53
3. 1_{k} 1_{i} 0_{+} 0 59  1^{2} 1_{i} 59∗ 59∗ 2 0_{+} ∗ ∗ 2  2 2
C_{2} 3  2  2 2  2 2
4. 1_{k} 1_{i} 0_{+} 0 2 -1 1^{2} 1_{i} 59∗ 59∗ 2 0_{+} ∗ ∗ 2 3 3 3 2 2  3
S_{3}  2 3 2 2 3 2 2 3

Discriminant class: 1

∞ 59 73 a_{1} a_{2} a_{3} Over p = 59 Over p = 73 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 53
5. 0_{+} 0_{+} 2_{+} -1 -24 27 3 0_{+} 1  1^{3} 2_{+} 1  3  3  3 3  3
C_{3}  3 3 3 3 3  3 3

Discriminant class: 73

∞ 59 73 a_{1} a_{2} a_{3} Over p = 59  Over p = 73 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 53
6. 0_{+} 0_{+} 1_{+} 0 -73  2 0_{+} ∗ ∗ 1^{2} 1_{+} 73 73  2 2 2 2 2
C_{2}  2 2  2 2 2