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.
- Canonical height
- Elliptic curve
- Linear dependence
- Pseudolinearly dependent point