When does an elliptic curve have accumulation points?

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If the rank of an elliptic curve is greater than 1,then it has infinitely many rational points,I wonder how are these rational points distributed, especially, can we find an elliptic curve such that there are infinitely many rational points when $xin (0,1)$?










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    As the rank is positive, the rational points are dense in their connected components as curve over $mathbbR$, so they are all accumulation points, see this paper.
    – Mercury
    Sep 10 at 12:45










  • @Mercury Many thanks!
    – Next
    Sep 10 at 14:37














up vote
3
down vote

favorite












If the rank of an elliptic curve is greater than 1,then it has infinitely many rational points,I wonder how are these rational points distributed, especially, can we find an elliptic curve such that there are infinitely many rational points when $xin (0,1)$?










share|cite|improve this question



















  • 2




    As the rank is positive, the rational points are dense in their connected components as curve over $mathbbR$, so they are all accumulation points, see this paper.
    – Mercury
    Sep 10 at 12:45










  • @Mercury Many thanks!
    – Next
    Sep 10 at 14:37












up vote
3
down vote

favorite









up vote
3
down vote

favorite











If the rank of an elliptic curve is greater than 1,then it has infinitely many rational points,I wonder how are these rational points distributed, especially, can we find an elliptic curve such that there are infinitely many rational points when $xin (0,1)$?










share|cite|improve this question















If the rank of an elliptic curve is greater than 1,then it has infinitely many rational points,I wonder how are these rational points distributed, especially, can we find an elliptic curve such that there are infinitely many rational points when $xin (0,1)$?







number-theory algebraic-number-theory diophantine-equations elliptic-curves






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edited Sep 10 at 10:38

























asked Sep 10 at 10:08









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  • 2




    As the rank is positive, the rational points are dense in their connected components as curve over $mathbbR$, so they are all accumulation points, see this paper.
    – Mercury
    Sep 10 at 12:45










  • @Mercury Many thanks!
    – Next
    Sep 10 at 14:37












  • 2




    As the rank is positive, the rational points are dense in their connected components as curve over $mathbbR$, so they are all accumulation points, see this paper.
    – Mercury
    Sep 10 at 12:45










  • @Mercury Many thanks!
    – Next
    Sep 10 at 14:37







2




2




As the rank is positive, the rational points are dense in their connected components as curve over $mathbbR$, so they are all accumulation points, see this paper.
– Mercury
Sep 10 at 12:45




As the rank is positive, the rational points are dense in their connected components as curve over $mathbbR$, so they are all accumulation points, see this paper.
– Mercury
Sep 10 at 12:45












@Mercury Many thanks!
– Next
Sep 10 at 14:37




@Mercury Many thanks!
– Next
Sep 10 at 14:37















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