New Sextic Fields Ramifying Above {5, 7}

Discriminant class: 5

∞ 5 7 a_{1} a_{2} a_{3} Over p = 5  Over p = 7 2 3 11 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. 2_{−} 9_{−} 4_{+} -2 -5 -5 1^{5} 9_{−} 5  1^{5} 4_{+} ∗  32 6 42 32 222 33 6 42
S_{6}  0 -1 52  3 6 42 222 32 2 42 3
2. 2_{−} 9_{−} 4_{+} -2 0 -10 1^{5} 9_{−} 5  1^{5} 4_{+} ∗  6 32 42 6 2 3 32 42
S_{6}  10 31 -37  33 32 42 2 6 222 42 33