Quartic Fields Unramified Outside of {∞, 5, 11}

Discriminant class: −55

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

Discriminant class: −11

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

Discriminant class: 1

∞ 5 11 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  2 3 7 13 17 19 23 29
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
3. 2_{−} 2_{+} 2_{−} 0 3 0 1^{2} 1_{+} 5 5 1^{2} 1_{i} 11∗ 11∗ 22 22 22 22 22 22 22 22
V_{4} 2 16 1^{2} 1_{+} 5 5 1^{2} 1_{i} 11∗ 11∗ 22 22 22 22 22 22

Discriminant class: 5

∞ 5 11 a_{1} a_{2} a_{3}  Over p = 5  Over p = 11  2 3 7 13 17 19 23 29
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
4. 2_{−} 3_{−} 0_{+} -1 1 -1 1^{4} 3_{−} 5 5  4 4 4 4 4 22 4 22
C_{4} 1 4 4 4 4 22
5. 0_{+} 3_{−} 2_{−} -1 -14 14 1^{4} 3_{−} 5 5 1^{2} 1_{i} 11∗ 11∗ 4 4 4 4 4  4
C_{4} 31 1^{2} 1_{i} 11∗ 11∗ 4 22 4 4 4 22 22
6. 2_{−} 1_{−} 2_{+} -1 1 1 1^{2} 1_{−} 5∗ 5∗ 2^{2} 2_{+} 1  V 4 2 4 4 4 22 2 22
D_{4} 1 2 0_{+} ∗ ∗ 22 2 22 4 2 2 22
7. 2_{−} 3_{−} 2_{+} 2 4 3 1^{4} 3_{−} 5 5 2^{2} 2_{+} 1  V 2 4 2 2 2 22 4 22
D_{4} 4  16  22 4 22 2 4 4 22 22