Low Degree Fields Ramifying Above {11, 13}

Discriminant class: −143

∞ 11 13 a_{1} a_{2} a_{3}  Over p = 11  Over p = 13  2 3 5 7 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} 1_{k} 1_{−} 0 143  1^{2} 1_{k} 11 11 1^{2} 1_{−} 13∗ 13∗  2  2  2
C_{2} 10  2 2  2 2  2 2

Discriminant class: 13

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