Low Degree Fields Ramifying Above {7, 11, 13}

Discriminant class: −143

∞ 7 11 13 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 13  2 3 5 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} 2_{+} 1_{k} 1_{−} -1 12 1 1^{3} 2_{+} 1  1^{2} 1_{k} 11 11 1^{2} 1_{−} 13∗ 13∗ 3 3 2 2  2 2
S_{3} 3  2 3 2 2  2 2 2

Discriminant class: −91

∞ 7 11 13 a_{1} a_{2} a_{3} Over p = 7  Over p = 11  Over p = 13  2 3 5 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. 1_{k} 1_{k} 2_{+} 1_{−} -1 -7 24 1^{2} 1_{k} 7 7 1^{3} 2_{+} ∗  1^{2} 1_{−} 13∗ 13∗ 2 2 3 2 3 3
S_{3} 2 3 3 3 3 2 2

Discriminant class: 1001

∞ 7 11 13 a_{1} a_{2} a_{3} Over p = 7 Over p = 11 Over p = 13 2 3 5 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
3. 0_{+} 1_{i} 1_{k} 1_{+} 0 -1001  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 11 11 1^{2} 1_{+} 13 13  2  2  2
C_{2} 2  2 2 2  2