Low Degree Fields Ramifying Above {11, 13, 23}

Discriminant class: −23

∞ 11 13 23 a_{1} a_{2}  a_{3} Over p = 11 Over p = 13  Over p = 23  2 3 5 7 17 19 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_{+} 2_{+} 1_{i} 0 143 1144 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗  3 2 2 2 2 3
S_{3} 3  2 3 2 3 2 3 2 2
2. 1_{k} 2_{+} 2_{+} 1_{i} -1 48 -53 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 2 2 3 3
S_{3} 3  2  2  2 3 2 2
3. 1_{k} 2_{+} 2_{+} 1_{i} -1 48 -1197 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{i} 23∗ 23∗ 3  2 2 2 2  3
S_{3} 3  2 3 2 3 2 3 2 2

Discriminant class: 3289

∞ 11 13 23 a_{1}  a_{2} a_{3}  Over p = 11  Over p = 13  Over p = 23  2 3 5 7 17 19 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
4. 0_{+} 1_{i} 1_{−} 1_{i} 0 -3289  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{i} 23∗ 23∗  2  2 2 2
C_{2} 2  2 2 2