Quartic Fields Unramified Outside of {∞, 23, 43}

Discriminant class: −43

∞ 23 43 a_{1} a_{2} a_{3} Over p = 23  Over p = 43  2 3 5 7 11 13 17 19
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 47 53 59 61
1. 1_{k} 2_{+} 3_{i}  -2 -20 21 2^{2} 2_{+} 1 V 1^{4} 3_{i} 43∗ 43 4 4 2 2 22 22 22 2
D_{4} -137 4 22 2 22 22 22 22 2

Discriminant class: −23

∞ 23 43 a_{1} a_{2} a_{3}  Over p = 23  Over p = 43  2 3 5 7 11 13 17 19
G h  a_{4}  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} 2_{+} -1 -1 6 1^{2} 1_{i} 23∗ 23∗ 1^{2} 1_{i} 43∗ 43∗ 3 3 4 2 4 3 4 4
S_{4} -7 1^{2} 1_{k} 43 43 3 3 2 3 3 4 22 4

Discriminant class: 1

∞ 23 43 a_{1} a_{2} a_{3}  Over p = 23  Over p = 43 2 3 5 7 11 13 17 19
G h  a_{4}  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 41 47 53 59 61
3. 2_{−} 2_{−} 2_{+} 0 33 0 1^{2} 1_{i} 23∗ 23∗ 2^{2} 2_{+} 1 V 22 22 22 22 22  22 22
V_{4} 3 25 1^{2} 1_{i} 23∗ 23∗ 22 22 22 22

Discriminant class: 989

∞ 23 43 a_{1} a_{2} a_{3}  Over p = 23  Over p = 43  2 3 5 7 11 13 17 19
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 47 53 59 61
4. 2_{−} 1_{k} 3_{k} -1 -5 -35 1^{2} 1_{k} 23 23 1^{4} 3_{k} 43 43∗ 4 4 22 22 2 22 2 22
D_{4}  107  2 0_{+} ∗ ∗  4 22 22 22 22 2 22 22