Low Degree Fields Unramified Outside of {∞, 17, 43}

Discriminant class: −731

∞ 17 43 a_{1} a_{2} a_{3}  Over p = 17  Over p = 43  2 3 5 7 11 13 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_{i} 0 731  1^{2} 1_{+} 17 17 1^{2} 1_{i} 43∗ 43∗ 2  2  2 2
C_{2} 12  2  2
2. 1_{k} 1_{+} 1_{i} -1 3 4 1^{2} 1_{+} 17 17 1^{2} 1_{i} 43∗ 43∗ 2 3 3  2 3 2 2
S_{3} 2  2 3 2 3 3 3 3

Discriminant class: −43

∞ 17 43 a_{1} a_{2} a_{3} Over p = 17  Over p = 43  2 3 5 7 11 13 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} 0_{+} 1_{i} 0 43  1^{2} 1_{i} 43∗ 43∗ 2 2 2 2  2
C_{2}  2  2  2

Discriminant class: 1

∞ 17 43 a_{1} a_{2} a_{3} Over p = 17 Over p = 43 2 3 5 7 11 13 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: 17

∞ 17 43 a_{1} a_{2} a_{3} Over p = 17 Over p = 43 2 3 5 7 11 13 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 -4  1^{2} 1_{+} 17 17  2 2 2 2  2
C_{2}  2 2 2 2  2