Low Degree Fields Ramifying Above {2, 11, 23}

Discriminant class: −506

∞ 2 11 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 23 3 5 7 13 17 19 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_{k} 1_{k} 1_{k} 0 506  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{k} 11 11 1^{2} 1_{k} 23 23  2  2
C_{2} 28  2  2  2 2

Discriminant class: −253

∞ 2 11 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 23 3 5 7 13 17 19 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} 2_{i} 1_{i} 1_{k} 0 253  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{k} 23 23 2 2 2 2  2 2 2
C_{2} 4  2 2 2 2 2 2

Discriminant class: −1

∞ 2 11 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11 Over p = 23 3 5 7 13 17 19 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} 2_{i} 2_{+} 2_{+} -1 -84 684 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2  2  3 2 3 2
S_{3} 6  3 3 2 2  2 3 2
4. 1_{k} 2_{i} 2_{+} 2_{+} -1 -84 -328 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  2 3 2 3 3 2  2
S_{3} 3  3  2 2 3 2 3 2

Discriminant class: 506

∞ 2 11 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  Over p = 23  3 5 7 13 17 19 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_{−} 1_{i} 1_{i} 0 -506  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{i} 23∗ 23∗ 2  2
C_{2} 6  2 2  2 2
6. 0_{+} 3_{−} 1_{i} 1_{i} -1 -10 -6 1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{i} 23∗ 23∗ 2 3 3 3 3 2 3 3
S_{3}  3 2 2 3  2 2 3