Low Degree Fields Ramifying Above {5, 7, 11}

Discriminant class: −55

∞ 5 7 11 a_{1} a_{2} a_{3} Over p = 5  Over p = 7  Over p = 11  2 3 13 17 19 23 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} 1_{+} 2_{+} 1_{i} 0 7 -7 1^{2} 1_{+} 5 5 1^{3} 2_{+} 1  1^{2} 1_{i} 11∗ 11∗ 3 2 3  2 2 2 3
S_{3} 3  2 2 3 2 2 3 2 2

Discriminant class: 385

∞ 5 7 11 a_{1} a_{2} a_{3}  Over p = 5  Over p = 7  Over p = 11  2 3 13 17 19 23 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. 0_{+} 1_{−} 1_{i} 1_{i} 0 -385  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{i} 11∗ 11∗  2 2  2 2 2
C_{2} 2  2  2 2  2