Mazur’s Growth Number Conjecture in the Rank One Case

Let p≥ 5 be a prime number. Let E/Q be an elliptic curve with good ordinary reduction at p. Let K be an imaginary quadratic field where p splits, and such that the generalized Heegner hypothesis holds. Under mild hypotheses, we show that if the p-adic height of the Heegner point of E over K is non-zero, then Mazur’s conjecture on the growth of Selmer coranks in the Zₚ²-extension of K holds.