Low Degree Fields Ramifying Above {2, 43}

Discriminant class: −86

∞ 2 43 a_{1} a_{2} a_{3} Over p = 2 Over p = 43 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 47 53 59 61
1. 1_{k} 3_{−} 1_{k} 0 86 1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 43 43 2 2 2
C_{2} 10  2 2

Discriminant class: −43

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

Discriminant class: −2

∞ 2 43 a_{1} a_{2} a_{3}  Over p = 2  Over p = 43 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 47 53 59 61
3. 1_{k} 3_{i} 2_{+} -1 -14 78 1^{2} 3_{i} −2 −2 1^{3} 2_{+} 1  2 2 3 2 3 3 2
S_{3} 3  2 2 2 3 2 2 3 2

Discriminant class: 43

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

Discriminant class: 86

∞ 2 43 a_{1} a_{2} a_{3}  Over p = 2  Over p = 43  3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d  s 29 31 37 41 47 53 59 61
5. 0_{+} 3_{k} 1_{i} 0 -86  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 43∗ 43∗ 2  2  2 2
C_{2}  2  2 2