Low Degree Fields Ramifying Above {5, 11, 13}

Discriminant class: −715

∞ 5 11 13 a_{1} a_{2} a_{3} Over p = 5 Over p = 11 Over p = 13 2 3 7 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_{−} 1_{k} 1_{+} 0 715 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 11 11 1^{2} 1_{+} 13 13 2 2 2 2 2 2
C_{2} 4  2 2 2

Discriminant class: −143

∞ 5 11 13 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 13  2 3 7 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} 2_{+} 1_{k} 1_{−} -1 -8 -33 1^{3} 2_{+} ∗  1^{2} 1_{k} 11 11 1^{2} 1_{−} 13∗ 13∗ 3  3 2 3 3 2 2
S_{3}  2  2 2 3 2 2 2

Discriminant class: −55

∞ 5 11 13 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 13 2 3 7 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. 1_{k} 1_{+} 1_{i} 2_{+} -1 -30 77 1^{2} 1_{+} 5 5 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} 1  3 2  3 2 2 2 3
S_{3} 3  2 2 3 2 2 3 2 2