Low Degree Fields Ramifying Above {3, 11, 17}

Discriminant class: −187

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 17  2 5 7 13 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} 4_{+} 1_{k} 1_{−} 0 6 -23 1^{3} 4_{+} ∗  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2 3 2 2 2 3 2
S_{3} 4 2 3 2 3 3

Discriminant class: −11

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 17 2 5 7 13 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} 4_{+} 1_{i} 2_{+} 0 51 -136 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 2 2 2 3 2 3
S_{3} 9  3 2 2  3 3 2 3
3. 1_{k} 4_{+} 1_{i} 2_{+} 0 -102 -629 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2  2 2 2 3 2 3
S_{3} 3  2 2 3 3  2 3

Discriminant class: −3

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3 Over p = 11 Over p = 17 2 5 7 13 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
4. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -187 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 3 2 2
S_{3} 3  3 2 3 2 2 2 3
5. 1_{k} 3_{i} 2_{+} 2_{+} 0 0 -2057 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 3 2 2 3
S_{3} 3  3 2 3 2 2 2 3 3
6. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -1683 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 3 2 2 3
S_{3} 3  3 2 3 2 2 2 3
7. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -9537 1^{3} 5_{i} 3∗ 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 2 3 2 2 3
S_{3} 24  3 2 3 2 2 2 3 3
8. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -6171 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2 3 3 3 2 2
S_{3} 3  2  2 2 2 3 3
9. 1_{k} 5_{i} 2_{+} 2_{+} 0 0 -561 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 2  3 3 2 2 3
S_{3} 48  2  2 2 2 3

Discriminant class: 561

∞ 3 11 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 11  Over p = 17 2 5 7 13 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
10. 0_{+} 1_{k} 1_{i} 1_{+} 0 -561  1^{2} 1_{k} 3 3 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 17 17  2 2  2 2
C_{2} 2  2 2 2 2 2 2