Low Degree Fields Ramifying Above {7, 67}

Discriminant class: −7

∞ 7 67 a_{1} a_{2} a_{3} Over p = 7 Over p = 67 2 3 5 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} 1_{i} 2_{+} -1 -22 -72 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} 1  2 2 3 2 2 2 3
S_{3} 15  3 2 3 2 3 2 3 2

Discriminant class: 1

∞ 7 67 a_{1} a_{2} a_{3} Over p = 7  Over p = 67 2 3 5 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. 0_{+} 2_{+} 2_{+} -1 -156 799 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3  3 3
C_{3} 3  3 3 3 3  3 3
3. 0_{+} 2_{+} 2_{+} 1 -156 608 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3
C_{3} 3  3  3  3 3 3

Discriminant class: 469

∞ 7 67 a_{1} a_{2} a_{3} Over p = 7  Over p = 67  2 3 5 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. 0_{+} 1_{k} 1_{i} 0 -469  1^{2} 1_{k} 7 7 1^{2} 1_{i} 67∗ 67∗ 2  2  2 2
C_{2} 3  2 2 2 2
5. 0_{+} 1_{k} 1_{i} -1 -5 4 1^{2} 1_{k} 7 7 1^{2} 1_{i} 67∗ 67∗ 2 3 3 2 3 2 2 3
S_{3}  3 3 3 3 2 2 2 2