Low Degree Fields Ramifying Above {2, 5, 11}

Discriminant class: −110

∞ 2 5 11 a_{1} a_{2} a_{3} Over p = 2 Over p = 5 Over p = 11 3 7 13 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_{−} 1_{k} 0 110  1^{2} 3_{+} 2 2 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 11 11  2  2
C_{2} 12  2 2 2  2
2. 1_{k} 3_{+} 1_{−} 1_{k} 0 2 -8 1^{2} 3_{+} 2 2 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 11 11 3 3 2 3 3 2 3 3
S_{3}  3 2 2 2 3 2 3

Discriminant class: −22

∞ 2 5 11 a_{1} a_{2} a_{3} Over p = 2 Over p = 5 Over p = 11 3 7 13 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_{−} 2_{+} 1_{k} 0 -5 -10 1^{2} 3_{−} 2∗ 2∗ 1^{3} 2_{+} ∗  1^{2} 1_{k} 11 11 2 2 3 2 3 3 3 3
S_{3} 2 2 3 2 2 2

Discriminant class: −5

∞ 2 5 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 11 3 7 13 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} 1_{+} 2_{+} -1 4 -20 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 5 5 1^{3} 2_{+} ∗  3 3 2 2 2  2
S_{3}  2 3 3 3 2 2 3 3

Discriminant class: 2

∞ 2 5 11 a_{1} a_{2} a_{3} Over p = 2 Over p = 5 Over p = 11 3 7 13 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
5. 0_{+} 3_{+} 2_{+} 2_{+} -1 -18 2 1^{2} 3_{+} 2 2 1^{3} 2_{+} ∗ 1^{3} 2_{+} ∗ 2 3 2 2 3 2 3
S_{3}  2 3 2 3 2 2 2 2

Discriminant class: 55

∞ 2 5 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 11 3 7 13 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_{+} 1_{k} 0 -55  1^{2} 2_{i} −1 −1 1^{2} 1_{+} 5 5 1^{2} 1_{k} 11 11  2  2 2
C_{2} 2  2 2 2  2 2 2

Discriminant class: 110

∞ 2 5 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  Over p = 11  3 7 13 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_{−} 1_{i} 0 -110  1^{2} 3_{i} −2 −2 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{i} 11∗ 11∗ 2 2 2  2  2
C_{2} 2  2  2