Old Sextic Fields Ramifying Above {7, 11}

Discriminant class: −11

∞ 7 11 a_{1} a_{2} a_{3} Over p = 7  Over p = 11 2 3 5 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} 4_{+} 3_{k} 1 4 3 2^{3} 4_{+} ∗  3^{2} 3_{k} 11∗  6 33 33 222 6 6 33 222
C_{6}  29 4 71  33 33 222 222 33 33 33 6

Discriminant class: 77

∞ 7 11 a_{1} a_{2} a_{3} Over p = 7  Over p = 11 2 3 5 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
2. 0_{+} 5_{i} 3_{k}  1 -20 -20 1^{6} 5_{i} 7  3^{2} 3_{k} 11∗  6 6 6  33 33 33 222
C_{6}  106 106 -83  6 33  222 6 33 6 33
3. 2_{−} 5_{i} 5_{i} -1 -6 -50 1^{6} 5_{i} 7  1^{6} 5_{i} 11∗  4 6 4 5 5 33 5 6
S_{5} 12  -13 6 64  4 5 33 4 222 5 4 5