Abstract
Let E be an elliptic curve defined overQ, and let T(E) denote the group ofQ-rational torsion points on E. In this article an explicit method for computing T(E) for all E with a given j-invariant j is given. In particular, if j≠0, 26 33 and E is defined by Y2=X3+AD2X+BD3 put into standard form with D its minimal D-factor, then a necessary condition that E possessQ-rational torsion points of order greater than 2 is that D|(22A3+33B2).
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Olson, L.D. Torsion points on elliptic curves with given j-invariant. Manuscripta Math 16, 145–150 (1975). https://doi.org/10.1007/BF01181637
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DOI: https://doi.org/10.1007/BF01181637