Old Sextic Fields Ramifying Above {13, 17}

Discriminant class: 17

∞ 13 17 a_{1} a_{2} a_{3} Over p = 13  Over p = 17 2 3 5 7 11 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. 0_{+} 4_{+} 3_{+} -1 -21 19 1^{3} 2_{+} 1  3^{2} 3_{+} 17  33 6 222 6 6 33 6 6
C_{6}  67 17 1 1^{3} 2_{+} 1  222 6 6 33  33 6

Discriminant class: 221

∞ 13 17 a_{1} a_{2} a_{3} Over p = 13  Over p = 17 2 3 5 7 11 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_{+} 3_{+} 1 -57 -56 1^{6} 5_{+} 13  3^{2} 3_{+} 17  6 6  33 33 6 6 6
C_{6} 2  526 55 -625  33 33 33 222  6 6