Low Degree Fields Ramifying Above {2, 11, 29}

Discriminant class: −638

∞ 2 11 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 29 3 5 7 13 17 19 23 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_{+} 0 638  1^{2} 3_{+} 2 2 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 29 29  2 2  2  2
C_{2} 20  2 2 2 2 2 2

Discriminant class: −58

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 29  3 5 7 13 17 19 23 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} 3_{k} 2_{+} 1_{−} 0 -11 -66 1^{2} 3_{k} −2∗ −2∗ 1^{3} 2_{+} ∗  1^{2} 1_{−} 29∗ 29∗ 2 2 2 2 2 2 2 3
S_{3} 3 2 2 2 3 3 3

Discriminant class: −11

∞ 2 11 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 11  Over p = 29 3 5 7 13 17 19 23 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} 2_{+} 1_{i} 2_{+} -1 -19 -43 1^{3} 2_{+} ∗  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3 3 2 2 2 2
S_{3} 3  3 2 2  3  2 3
4. 1_{k} 2_{+} 1_{i} 2_{+} 0 -58 -174 1^{3} 2_{+} ∗  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3 2 2 2 2 3 3
S_{3} 3  2 2  3 3 2

Discriminant class: 29

∞ 2 11 29 a_{1} a_{2} a_{3} Over p = 2 Over p = 11 Over p = 29 3 5 7 13 17 19 23 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
5. 0_{+} 2_{+} 2_{+} 1_{+} -1 -29 -31 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 1^{2} 1_{+} 29 29 2 3 3 2 2 3 2
S_{3}  2 2 2 2 3 3 2

Discriminant class: 319

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 29  3 5 7 13 17 19 23 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 -319  1^{2} 2_{i} −1 −1 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{−} 29∗ 29∗  2  2 2
C_{2} 2  2  2  2  2

Discriminant class: 638

∞ 2 11 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 29 3 5 7 13 17 19 23 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 -638  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 11 11 1^{2} 1_{+} 29 29 2 2  2
C_{2} 2  2  2