Effective results on linear dependence for elliptic curves

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Given a subgroup Γ of rational points on an elliptic curve E defined over ℚ of rank r ≥ 1 and any sufficiently large x ≥ 2, assuming that the rank of Γ is less than r, we give upper and lower bounds on the canonical height of a rational point Q which is not in the group 0 but belongs to the reduction of Γ modulo every prime p ≤ x of good reduction for E.

Original languageEnglish
Pages (from-to)123-144
Number of pages22
JournalPacific Journal of Mathematics
Issue number1
Publication statusPublished - 2018
Externally publishedYes


  • Canonical height
  • Elliptic curve
  • Linear dependence
  • Pseudolinearly dependent point
  • Pseudomultiple


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