New Sextic Fields Ramifying Above {3, 11}

Discriminant class: −11

∞ 3 11 a_{1} a_{2} a_{3} Over p = 3 Over p = 11 2 5 7 13 17 19 23 29
G h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 3_{i} 8_{+} 3_{k} 0 3 -2 2^{3} 8_{+} 1  1^{3} 2_{+} ∗  32 5 6 4 6 32 42 6
S_{6}  6 9 5  1^{2} 1_{k} 11 11 5 5 4 32 22 33 42 32
2. 1_{k} 8_{+} 5_{i} 0 0 -44 2^{3} 8_{+} 1  1^{6} 5_{i} 11∗  6 5 32 4 32 6 42 32
S_{6}  99 -66 11  5 5 4 6 22 3 42 6

Discriminant class: −3

∞  3 11 a_{1} a_{2} a_{3}  Over p = 3  Over p = 11  2 5 7 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
3. 3_{i}  3_{k} 4_{+} 0 1 -2 1^{3} 3_{k} 3  1^{4} 3_{k} 11 11∗ 6 32 42 42 6 42 32 6
C_{3}^{2}.D_{4}  3 -1 1 2 0_{+} ∗ ∗ 1^{2} 1_{i} 11∗ 11∗ 22 22 6 42 32 32 32 42
4. 1_{k}  7_{i} 4_{+} -3 -6 22 1^{6} 7_{i} 3∗  1^{4} 3_{i} 11∗ 11 32 6 42 42 32 42 6 32
C_{3}^{2}.D_{4}  0 -33 22  1^{2} 1_{k} 11 11 22 22 32 42 6 6 6 42

Discriminant class: 33

∞  3 11 a_{1} a_{2} a_{3}  Over p = 3  Over p = 11  2 5 7 13 17 19 23 29
G  h  a_{4} a_{5} a_{6} f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
5. 2_{−} 9_{i} 3_{i}  0 3 -2 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  5 6 6 4 5 6 6 42
S_{6}  6 9 -6 1^{3} 4_{+} 1  1^{2} 1_{i} 11∗ 11∗ 42 3 5 4 4 4 6 6
6. 2_{−} 11_{k} 5_{k} 0 0 99 1^{6} 11_{k} 3∗  1^{6} 5_{k} 11  5 32 32 4 5 32 32 42
S_{6}  2  -99 198 561  42 33 5 4 4 4 32 32