Quartic Fields Unramified Outside of {∞, 11, 43}

Discriminant class: −43

∞ 11 43 a_{1} a_{2} a_{3} Over p = 11  Over p = 43  2 3 5 7 13 17 19 23
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 2 4 4 2 22 22 2
D_{4} 3 -8 2 22 4 22 22 2

Discriminant class: 1

∞ 11 43 a_{1} a_{2} a_{3}  Over p = 11  Over p = 43 2 3 5 7 13 17 19 23
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. 2_{−} 2_{−} 2_{+} 0 27 0 1^{2} 1_{i} 11∗ 11∗ 2^{2} 2_{+} 1 V 22 22 22 22 22 22 22
V_{4} 3  64  1^{2} 1_{i} 11∗ 11∗  22  22 22  22
3. 0_{+} 2_{+} 2_{+} -1 -16 -7 2^{2} 2_{+} 1  V 1^{3} 2_{+} 1  22 3 3 3 3 3 3 3
A_{4}  27  3 3 3 22 22 3 22 3

Discriminant class: 473

∞ 11 43 a_{1} a_{2} a_{3}  Over p = 11  Over p = 43  2 3 5 7 13 17 19 23
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 8 1^{2} 1_{k} 11 11 1^{4} 3_{k} 43 43∗ 22 4 4 22 2 2 22
D_{4} 64 2 0_{+} ∗ ∗ 22 22 4 2 22 22
5. 2_{−} 3_{i} 1_{i}  1 10 9 1^{4} 3_{i} 11∗ 11 1^{2} 1_{i} 43∗ 43∗ 3 2 4 3 2 2 3 3
S_{4} 2 26 2 0_{+} ∗ ∗ 3 3 4 4 3 3 3 3
6. 2_{−} 1_{k} 3_{k}  -1 -5 8 1^{2} 1_{k} 11 11 1^{4} 3_{k} 43 43∗ 3 2 2 3 4 2 3 3
S_{4} 2 21 2 0_{+} ∗ ∗ 3 3 4 4 3 3 3 3
7. 0_{+} 3_{i} 3_{k}  1 -177 680 1^{4} 3_{i} 11∗ 11 1^{4} 3_{k} 43 43∗ 3 2 4 3 4 2 3 3
S_{4} 2  -667  3 3 2 2 3 3 3 3