Low Degree Fields Ramifying Above {3, 11}

Discriminant class: −11

∞ 3 11 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  2 5 7 13 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} 4_{+} 1_{i} 0 6 -1 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 2 3 2 2 2 2  2
S_{3} 3  3 3 2 2 3 3 3 2

Discriminant class: −3

∞ 3 11 a_{1} a_{2} a_{3} Over p = 3 Over p = 11 2 5 7 13 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. 1_{k} 3_{i} 2_{+} 0 0 -11 1^{3} 3_{i} 3∗  1^{3} 2_{+} ∗  2 2 3 3 2  2 2
S_{3} 2  3  2  2 2 2
3. 1_{k} 5_{i} 2_{+} 0 0 -99 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2  2 3 2 2
S_{3}  3 3 2 3 2 2 2
4. 1_{k} 5_{i} 2_{+} 0 0 -33 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 2 2 3 3 2 3 2 2
S_{3}  3 2 3 2 2 2

Discriminant class: 33

∞ 3 11 a_{1} a_{2} a_{3} Over p = 3 Over p = 11 2 5 7 13 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
5. 0_{+} 1_{i} 1_{k} 0 -33 1^{2} 1_{i} 3∗ 3∗ 1^{2} 1_{k} 11 11 2 2 2 2 2
C_{2}  2 2 2 2 2
6. 0_{+} 5_{i} 1_{k} 0 -9 -3 1^{3} 5_{i} 3∗  1^{2} 1_{k} 11 11 3 2 2 2 3 2 2 3
S_{3}  3 3 2 2 2 2 2