Low Degree Fields Ramifying Above {2, 73}

Discriminant class: −146

∞ 2 73 a_{1} a_{2} a_{3}  Over p = 2  Over p = 73 3 5 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 53 59
1. 1_{k} 3_{i} 1_{+} 0 146  1^{2} 3_{i} −2 −2 1^{2} 1_{+} 73 73  2  2  2
C_{2} 16  2  2  2

Discriminant class: −73

∞ 2 73 a_{1} a_{2} a_{3}  Over p = 2  Over p = 73 3 5 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 53 59
2. 1_{k} 2_{i} 1_{+} 0 73  1^{2} 2_{i} −1 −1 1^{2} 1_{+} 73 73 2 2  2 2 2 2
C_{2} 4  2  2

Discriminant class: −2

∞ 2 73 a_{1} a_{2} a_{3}  Over p = 2  Over p = 73 3 5 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 53 59
3. 1_{k} 3_{i} 2_{+} -1 -24 100 1^{2} 3_{i} −2 −2 1^{3} 2_{+} 1  3 2 2 3 2  2
S_{3} 3  2 2 2 3 3 2 2 3

Discriminant class: −1

∞ 2 73 a_{1} a_{2} a_{3}  Over p = 2  Over p = 73 3 5 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 53 59
4. 1_{k} 2_{i} 2_{+} -1 -24 -46 1^{2} 2_{i} −1 −1 1^{3} 2_{+} 1  2  2 2 3 3 2 2
S_{3} 3  3 2 3 3 2 2  2

Discriminant class: 146

∞ 2 73 a_{1} a_{2} a_{3} Over p = 2  Over p = 73 3 5 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 53 59
5. 0_{+} 3_{+} 1_{+} 0 -146  1^{2} 3_{+} 2 2 1^{2} 1_{+} 73 73 2  2  2 2
C_{2} 2  2 2  2