Low Degree Fields Unramified Outside of {∞, 7, 43}

Discriminant class: −43

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

Discriminant class: −7

∞ 7 43 a_{1} a_{2} a_{3} Over p = 7 Over p = 43 2 3 5 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} 1_{i} 0_{+} 1 2  1^{2} 1_{i} 7∗ 7∗  2 2  2 2 2
C_{2}  2  2 2  2 2
3. 1_{k} 1_{i} 2_{+} -1 -14 35 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} 1  3 2 2  2 2 2 3
S_{3} 3  3 2  2 2  2 2

Discriminant class: 1

∞ 7 43 a_{1} a_{2} a_{3} Over p = 7  Over p = 43 2 3 5 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_{+} 0_{+} -1 -2  1 1^{3} 2_{+} 1  3 3 3 3  3 3 3
C_{3}  3 3  3 3 3 3
5. 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
6. 0_{+} 2_{+} 2_{+} -1 -100 -223 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3
C_{3} 3  3 3  3 3 3 3
7. 0_{+} 2_{+} 2_{+} -1 -100 379 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3 3 3 3
C_{3} 3  3  3  3  3

Discriminant class: 301

∞ 7 43 a_{1} a_{2} a_{3} Over p = 7  Over p = 43  2 3 5 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
8. 0_{+} 1_{k} 1_{i} 0 -301  1^{2} 1_{k} 7 7 1^{2} 1_{i} 43∗ 43∗ 2  2 2
C_{2}  2 2 2 2 2  2