New Sextic Fields Ramifying Above {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} 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. 1_{k}  5_{−} 3_{k} -1 -5 -5 1^{6} 5_{−} 5  1^{3} 2_{+} ∗  42 6 42 42 42 32 6 32
C_{3}^{2}.D_{4}  15 14 1  1^{2} 1_{k} 11 11 22 6 32 42 6 222 3 2
2. 3_{i}  3_{−} 5_{i} -2 -2 7 1^{3} 2_{+} ∗  1^{6} 5_{i} 11∗  42 32 42 42 42 6 32 6
C_{3}^{2}.D_{4}  1 -6 4 1^{2} 1_{−} 5∗ 5∗  22 32 6 42 32 2 33 222

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} 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. 2_{−} 9_{−} 2_{+} 0 -10 -5 1^{5} 9_{−} 5  1^{3} 2_{+} ∗  6 32 32 4 222 5 6 42
S_{6}  30 28 5  2 0_{+} ∗ ∗ 42 4 42 32 32 4 5 5
4. 2_{−} 9_{−} 4_{+} 3 -25 0 1^{5} 9_{−} 5  1^{3} 2_{+} ∗  32 6 6 4 2 5 32 42
S_{6}  325 -395 -85  1^{3} 2_{+} ∗  42 4 42 6 6 4 5 5