Low Degree Fields Ramifying Above {2, 23}

Discriminant class: −46

∞ 2 23 a_{1} a_{2} a_{3} Over p = 2  Over p = 23  3 5 7 11 13 17 19 29
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
1. 1_{k} 3_{+} 1_{i} 0 46  1^{2} 3_{+} 2 2 1^{2} 1_{i} 23∗ 23∗ 2  2  2 2  2
C_{2} 4  2

Discriminant class: −2

∞ 2 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23 3 5 7 11 13 17 19 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
2. 1_{k} 3_{i} 2_{+} -1 -15 -29 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  3 2 2  2 3 3 2
S_{3}  2 2  3 2 2 3 2

Discriminant class: −1

∞ 2 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23 3 5 7 11 13 17 19 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 1_{k} 2_{i} 2_{+} -1 8 -6 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  2 3 2 2 3  2 3
S_{3} 2  2  3 2 2 3 2 3

Discriminant class: 23

∞ 2 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23 3 5 7 11 13 17 19 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
4. 0_{+} 2_{i} 1_{k} 0 -23  1^{2} 2_{i} −1 −1 1^{2} 1_{k} 23 23 2 2  2
C_{2}  2 2  2 2 2 2

Discriminant class: 46

∞ 2 23 a_{1} a_{2} a_{3}  Over p = 2  Over p = 23 3 5 7 11 13 17 19 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
5. 0_{+} 3_{i} 1_{k} 0 -46  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 23 23  2 2 2 2 2
C_{2}  2  2 2