Low Degree Fields Ramifying Above {2, 7}

Discriminant class: −14

∞ 2 7 a_{1} a_{2} a_{3} Over p = 2 Over p = 7 3 5 11 13 17 19 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 1_{k} 3_{+} 1_{i} 0 14 1^{2} 3_{+} 2 2 1^{2} 1_{i} 7∗ 7∗ 2 2 2
C_{2} 4  2 2 2 2 2 2

Discriminant class: 7

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

Discriminant class: 14

∞ 2 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7 3 5 11 13 17 19 23 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 0_{+} 3_{i} 1_{k} 0 -14  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 7 7 2  2 2 2 2
C_{2}  2 2  2 2