Low Degree Fields Unramified Outside of {∞, 5, 43}

Discriminant class: −215

∞ 5 43 a_{1} a_{2} a_{3} Over p = 5 Over p = 43 2 3 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} 1_{−} 1_{k} 0 215  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 43 43  2 2 2 2
C_{2} 14  2  2 2  2

Discriminant class: −43

∞ 5 43 a_{1} a_{2} a_{3} Over p = 5  Over p = 43  2 3 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} 0_{+} 1_{i} 0 43  2 0_{+} ∗ ∗ 1^{2} 1_{i} 43∗ 43∗ 2 2 2  2
C_{2}  2  2  2
3. 1_{k} 2_{+} 1_{i} -1 2 12 1^{3} 2_{+} ∗  1^{2} 1_{i} 43∗ 43∗ 2 2 2 3 3  2 3
S_{3}  2 3 2 3 3 3 3 2

Discriminant class: 1

∞ 5 43 a_{1} a_{2} a_{3} Over p = 5  Over p = 43 2 3 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_{+} 0_{+} 2_{+} -1 -14 -8 3 0_{+} 1  1^{3} 2_{+} 1  3 3  3 3 3 3
C_{3}  3 3 3  3  3

Discriminant class: 5

∞ 5 43 a_{1} a_{2} a_{3} Over p = 5  Over p = 43 2 3 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_{+} 1_{+} 0_{+} 1 -1  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 2 2 2  2 2  2
C_{2}  2  2 2