New Sextic Fields Unramified Outside of {∞, 13, 19}

Discriminant class: 1

∞ 13 19 a_{1} a_{2} a_{3} Over p = 13  Over p = 19  2 3 5 7 11 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. 2_{−} 2_{+} 4_{−} 0 -4 -15 1^{3} 2_{+} 1  1^{4} 3_{k} 19 19∗ 42 5 5 42 5 33 5 3
A_{6} -15 -8 4 3 0_{+} 1 1^{2} 1_{k} 19 19 3 3 42 42 42 5 5 42
2. 2_{−} 4_{+} 4_{−} -2 10 -34 1^{3} 2_{+} 1  1^{4} 3_{i} 19∗ 19 42 5 5 42 5 3 5 33
A_{6} 3  -26 182 -143 1^{3} 2_{+} 1  1^{2} 1_{i} 19∗ 19∗ 33 33 42 42 42 5 5 42