Low Degree Fields Ramifying Above {2, 7, 23}

Discriminant class: −322

∞ 2 7 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7  Over p = 23 3 5 11 13 17 19 29 31
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
1. 1_{k} 3_{i} 1_{i} 1_{k} 0 322  1^{2} 3_{i} −2 −2 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 23 23 2 2 2  2
C_{2} 8  2 2  2 2 2

Discriminant class: −161

∞ 2 7 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7  Over p = 23 3 5 11 13 17 19 29 31
G h  f^{e} c_{w} d  s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
2. 1_{k} 2_{i} 1_{i} 1_{k} 0 161  1^{2} 2_{i} −1 −1 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 23 23  2  2
C_{2} 16  2 2  2

Discriminant class: 322

∞ 2 7 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 7  Over p = 23  3 5 11 13 17 19 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
3. 0_{+} 3_{+} 1_{k} 1_{i} 0 -322  1^{2} 3_{+} 2 2 1^{2} 1_{k} 7 7 1^{2} 1_{i} 23∗ 23∗  2  2 2 2
C_{2} 4  2  2  2