Could someone please explain how to apply the Nagell-Lutz theorem to non-Weierstrass normal form elliptic curves in order to find all the torsion points / points of finite order. If the answer to this is to simply convert to Weierstrass form, could this transformation please be explained in simple terms?



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    $\begingroup$ The answer is to convert (birationally) to the Weierstrass normal form, since the result en.wikipedia.org/wiki/Nagell%E2%80%93Lutz_theorem (and its generalization in loc. cit.) wants this form. The transformation is rather standard, but we need an elliptic curve equation and a (rational) point on the curve. Is the most general cubic the start? Take a look at Ian Connell's excelent exposition webs.ucm.es/BUCM/mat/doc8354.pdf, Cubic to Weierstrass. $\endgroup$
    – dan_fulea
    Dec 1, 2020 at 12:25


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