Low Degree Fields Ramifying Above {2, 11, 13}

Discriminant class: −286

∞ 2 11 13 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 13 3 5 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} 3_{+} 1_{i} 1_{+} 0 286  1^{2} 3_{+} 2 2 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 13 13 2  2 2  2
C_{2} 12  2 2
2. 1_{k} 3_{+} 1_{i} 1_{+} -1 6 2 1^{2} 3_{+} 2 2 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 13 13 2 3 3 2 2 3 3 2
S_{3}  3 3 2 2 3 3 3

Discriminant class: −22

∞ 2 11 13 a_{1} a_{2} a_{3} Over p = 2 Over p = 11 Over p = 13 3 5 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} 3_{−} 1_{k} 2_{+} -1 22 -66 1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 11 11 1^{3} 2_{+} 1  2 2 2 2 3 3 3
S_{3} 9 2 2 3 3 2 2 2

Discriminant class: −1

∞ 2 11 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11 Over p = 13 3 5 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
4. 1_{k} 2_{i} 2_{+} 2_{+} -1 48 -196 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2 3 2  2 2 3 2
S_{3} 6  2 2  2 3 2
5. 1_{k} 2_{i} 2_{+} 2_{+} -1 48 90 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  2  2 3 2 2  2
S_{3} 3  3 3 2 2 3 2 3 2

Discriminant class: 143

∞ 2 11 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 13  3 5 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
6. 0_{+} 2_{i} 1_{i} 1_{−} 0 -143  1^{2} 2_{i} −1 −1 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 13∗ 13∗ 2 2 2 2 2 2 2
C_{2} 2 2 2

Discriminant class: 286

∞ 2 11 13 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 13 3 5 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
7. 0_{+} 3_{i} 1_{k} 1_{+} 0 -286  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 11 11 1^{2} 1_{+} 13 13  2 2  2
C_{2} 2  2  2 2  2