New Sextic Fields Unramified Outside of {∞, 2, 19}

Discriminant class: −2

∞  2 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  3 5 7 11 13 17 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} 11_{i} 4_{−} -2  2 0 1^{4} 11_{i} −2 2 1^{4} 3_{i} 19∗ 19 5 32 6 42 4 5 4 32
S_{6} 2 -15 10 24 1^{2} 1_{i} 19∗ 19∗ 32 32 42 22 6 32 42 6
2. 1_{k} 13_{k} 4_{−} 2 -8 48 1^{4} 11_{−} 2 −2 1^{4} 3_{k} 19 19∗ 5 6 32 42 4 5 4 6
S_{6}  63 -190 38 1^{2} 2_{i} −1 −1 1^{2} 1_{k} 19 19 6 6 42 22 32 6 42 32