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In the Proof of Mordell Conjecture by Gerd Faltings, it is famous that Parshin constructed curve C_P for each Q-rational point P on the given curve C over Q such that genus of C satisfies g(C) > 0.

Is there anybody that, in case C = E elliptic curve over Q, gives me explicite construction

C_P ---> E

together with Q-rational point P on E?

I am quite anxious for an explicite example of Parshin's construction. Many thanks. Sincerely yours, Pierre MATSUMI

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Would your question be answered by Lemma 5.3 in J. S. Milne's text on abelian varieties, and the discussion preceding it? Here is the link: –  Vesselin Dimitrov Sep 27 '13 at 15:37

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